Learning Goal: To gain insight into the independence of the scalar triple product from the point on the line chosen as the reference point of the calculation. The magnitude of a moment about a line segment connecting points P and Q due to a force F applied at point R (with R not on the line through P and Q) can be calculated using the scalar triple product, MpQupq rx F, where r is a position vector from any point on the line through P and Q to R and upo is the unit vector in the direction of line segment PQ. The unit vector upq is then multiplied by this magnitude to find the vector representation of the moment. As shown in the figure, the member is anchored at A and section AB lies in the x-y plane. The dimensions are ₁ = 1.2 m, y₁ = 1.8 m, and z₁ = 1.6 m. The force applied at point C is F=[-170 i+ 105 j + 110 k] N. Figure B 1 of 1 > Using the position vector from B to C, calculate the moment about segment AB due to force F. Express the individual components to three significant figures, if necessary, separated by commas. ▾ View Available Hint(s) Hint 1. Calculating the moment about a line segment The scalar triple product of the unit direction vector of the line segment, direction vector to the force, and the force vector gives the magnitude of the moment. To ensure the moment vector lies along the line segment, multiply the magnitude by the unit direction vector of the line segment. ▼ Hint 2. Find the unit vector in the direction of segment AB Because segment AB lies in the x-y plane, there is no z component in the position vector AB. What is the unit vector from A to B, UAB. Express the individual components to three significant figures, if necessary, separated by commas. ► View Available Hint(s) UAB = Submit VE ΑΣΦ vec SE ? i, j Hint 3. Find the position vector BC What is the position vector from B to C? Express the individual components to three significant figures, if necessary, separated by commas.
Learning Goal: To gain insight into the independence of the scalar triple product from the point on the line chosen as the reference point of the calculation. The magnitude of a moment about a line segment connecting points P and Q due to a force F applied at point R (with R not on the line through P and Q) can be calculated using the scalar triple product, MpQupq rx F, where r is a position vector from any point on the line through P and Q to R and upo is the unit vector in the direction of line segment PQ. The unit vector upq is then multiplied by this magnitude to find the vector representation of the moment. As shown in the figure, the member is anchored at A and section AB lies in the x-y plane. The dimensions are ₁ = 1.2 m, y₁ = 1.8 m, and z₁ = 1.6 m. The force applied at point C is F=[-170 i+ 105 j + 110 k] N. Figure B 1 of 1 > Using the position vector from B to C, calculate the moment about segment AB due to force F. Express the individual components to three significant figures, if necessary, separated by commas. ▾ View Available Hint(s) Hint 1. Calculating the moment about a line segment The scalar triple product of the unit direction vector of the line segment, direction vector to the force, and the force vector gives the magnitude of the moment. To ensure the moment vector lies along the line segment, multiply the magnitude by the unit direction vector of the line segment. ▼ Hint 2. Find the unit vector in the direction of segment AB Because segment AB lies in the x-y plane, there is no z component in the position vector AB. What is the unit vector from A to B, UAB. Express the individual components to three significant figures, if necessary, separated by commas. ► View Available Hint(s) UAB = Submit VE ΑΣΦ vec SE ? i, j Hint 3. Find the position vector BC What is the position vector from B to C? Express the individual components to three significant figures, if necessary, separated by commas.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![Learning Goal:
To gain insight into the independence of the scalar
triple product from the point on the line chosen as the
reference point of the calculation.
The magnitude of a moment about a line segment
connecting points P and Q due to a force F applied at
point R (with R not on the line through P and Q) can
be calculated using the scalar triple product,
MpQupq r × F,
=
where r is a position vector from any point on the line
through P and Q to R and upq is the unit vector in the
direction of line segment PQ. The unit vector upq is
then multiplied by this magnitude to find the vector
representation of the moment.
As shown in the figure, the member is anchored at A
and section AB lies in the x-y plane. The dimensions
are x₁ = 1.2 m, y₁ = 1.8 m, and 2₁ = 1.6 m. The
force applied at point C is
F = [-170 i +105 j + 110 k] N.
Figure
B
1 of 1
Using the position vector from B to C, calculate the moment about segment AB due to force F.
Express the individual components to three significant figures, if necessary, separated by commas.
View Available Hint(s)
Hint 1. Calculating the moment about a line segment
The scalar triple product of the unit direction vector of the line segment, direction vector to the force, and the force vector gives
the magnitude of the moment. To ensure the moment vector lies along the line segment, multiply the magnitude by the unit
direction vector of the line segment.
Hint 2. Find the unit vector in the direction of segment AB
Because segment AB lies in the x-y plane, there is no z component in the position vector AB. What is the unit vector from A
to B, UAB.
Express the individual components to three significant figures, if necessary, separated by commas.
► View Available Hint(s)
UAB
||
Submit
呃
V—| ΑΣΦ | 1
vec
X
?
i, j
Hint 3. Find the position vector BC
What is the position vector from B to C?
Express the individual components to three significant figures, if necessary, separated by commas.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51980497-9ac6-412d-a3a8-b7288358dac3%2F8a27a3d2-9b1e-4f02-bb70-87322bef5d14%2F3g92mrl_processed.png&w=3840&q=75)
Transcribed Image Text:Learning Goal:
To gain insight into the independence of the scalar
triple product from the point on the line chosen as the
reference point of the calculation.
The magnitude of a moment about a line segment
connecting points P and Q due to a force F applied at
point R (with R not on the line through P and Q) can
be calculated using the scalar triple product,
MpQupq r × F,
=
where r is a position vector from any point on the line
through P and Q to R and upq is the unit vector in the
direction of line segment PQ. The unit vector upq is
then multiplied by this magnitude to find the vector
representation of the moment.
As shown in the figure, the member is anchored at A
and section AB lies in the x-y plane. The dimensions
are x₁ = 1.2 m, y₁ = 1.8 m, and 2₁ = 1.6 m. The
force applied at point C is
F = [-170 i +105 j + 110 k] N.
Figure
B
1 of 1
Using the position vector from B to C, calculate the moment about segment AB due to force F.
Express the individual components to three significant figures, if necessary, separated by commas.
View Available Hint(s)
Hint 1. Calculating the moment about a line segment
The scalar triple product of the unit direction vector of the line segment, direction vector to the force, and the force vector gives
the magnitude of the moment. To ensure the moment vector lies along the line segment, multiply the magnitude by the unit
direction vector of the line segment.
Hint 2. Find the unit vector in the direction of segment AB
Because segment AB lies in the x-y plane, there is no z component in the position vector AB. What is the unit vector from A
to B, UAB.
Express the individual components to three significant figures, if necessary, separated by commas.
► View Available Hint(s)
UAB
||
Submit
呃
V—| ΑΣΦ | 1
vec
X
?
i, j
Hint 3. Find the position vector BC
What is the position vector from B to C?
Express the individual components to three significant figures, if necessary, separated by commas.
![Learning Goal:
To gain insight into the independence of the scalar
triple product from the point on the line chosen as the
reference point of the calculation.
The magnitude of a moment about a line segment
connecting points P and Q due to a force F applied at
point R (with R not on the line through P and Q) can
be calculated using the scalar triple product,
MPQ
= = upq r x F,
where r is a position vector from any point on the line
through P and Q to R and up is the unit vector in the
direction of line segment PQ. The unit vector upq is
then multiplied by this magnitude to find the vector
representation of the moment.
As shown in the figure, the member is anchored at A
and section AB lies in the x-y plane. The dimensions
are x₁ = 1.2 m, y₁ = 1.8 m, and z1₁ = 1.6 m. The
force applied at point C is
F = [-170 i +105 j + 110 k] N.
Figure
B
1 of 1
Using the position vector from A to C, calculate the moment about segment AB due to force F.
Express the individual components to three significant figures, if necessary, separated by commas.
View Available Hint(s)
Hint 1. Calculating the moment about a line segment
The scalar triple product of the unit direction vector of the line segment, direction vector to the force, and the force vector gives
the magnitude of the moment. To ensure the moment vector lies along the line segment, multiply the magnitude by the unit
direction vector of the line segment.
Hint 2. Find the unit vector in the direction of segment AB
Because segment AB lies in the x-y plane, there is no z component in the position vector AB. What is the unit vector from A
to B, UAB?
Express the individual components to three significant figures, if necessary, separated by commas.
UAB
Submit
VG| ΑΣΦ |
VO
Request Answer
↓↑ vec
?
i, j
Hint 3. Find the position vector AC
What is the position vector from A to C?
Express the individual components to three significant figures, if necessary, separated by commas.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F51980497-9ac6-412d-a3a8-b7288358dac3%2F8a27a3d2-9b1e-4f02-bb70-87322bef5d14%2Fxtnpdsz_processed.png&w=3840&q=75)
Transcribed Image Text:Learning Goal:
To gain insight into the independence of the scalar
triple product from the point on the line chosen as the
reference point of the calculation.
The magnitude of a moment about a line segment
connecting points P and Q due to a force F applied at
point R (with R not on the line through P and Q) can
be calculated using the scalar triple product,
MPQ
= = upq r x F,
where r is a position vector from any point on the line
through P and Q to R and up is the unit vector in the
direction of line segment PQ. The unit vector upq is
then multiplied by this magnitude to find the vector
representation of the moment.
As shown in the figure, the member is anchored at A
and section AB lies in the x-y plane. The dimensions
are x₁ = 1.2 m, y₁ = 1.8 m, and z1₁ = 1.6 m. The
force applied at point C is
F = [-170 i +105 j + 110 k] N.
Figure
B
1 of 1
Using the position vector from A to C, calculate the moment about segment AB due to force F.
Express the individual components to three significant figures, if necessary, separated by commas.
View Available Hint(s)
Hint 1. Calculating the moment about a line segment
The scalar triple product of the unit direction vector of the line segment, direction vector to the force, and the force vector gives
the magnitude of the moment. To ensure the moment vector lies along the line segment, multiply the magnitude by the unit
direction vector of the line segment.
Hint 2. Find the unit vector in the direction of segment AB
Because segment AB lies in the x-y plane, there is no z component in the position vector AB. What is the unit vector from A
to B, UAB?
Express the individual components to three significant figures, if necessary, separated by commas.
UAB
Submit
VG| ΑΣΦ |
VO
Request Answer
↓↑ vec
?
i, j
Hint 3. Find the position vector AC
What is the position vector from A to C?
Express the individual components to three significant figures, if necessary, separated by commas.
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