Suppose vector i = (-3,4,-6] and originates at point A at (1,5,-3) and terminates at point B at (3,6,9) a. Find vector and write it in both ordered pair and unit vector notation b. Find a normal to vectors and c. Find a unit vector that is the same magnitude as the normal you obtained in question 2, part b. Use the dot product to verify that the normal you obtained in question 2, part b is orthogonal to both vectors i and d. e. Suppose vectors and are both direction vectors in a plane that also contains the point (2,-4,7). Determine: L ii. A vector equation for the plane Parametric equations for the plane A scalar equation for the plane
Suppose vector i = (-3,4,-6] and originates at point A at (1,5,-3) and terminates at point B at (3,6,9) a. Find vector and write it in both ordered pair and unit vector notation b. Find a normal to vectors and c. Find a unit vector that is the same magnitude as the normal you obtained in question 2, part b. Use the dot product to verify that the normal you obtained in question 2, part b is orthogonal to both vectors i and d. e. Suppose vectors and are both direction vectors in a plane that also contains the point (2,-4,7). Determine: L ii. A vector equation for the plane Parametric equations for the plane A scalar equation for the plane
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please help me with this. Please check if I've gotten the write answer for each questions. And if I have shown the correct steps. Just check question c), d) and e)
Just write the answers that are correct (e.g. a) correct, b) incorrect, etc)
Image 1: The question
Image 2: My work
![Criven that. I [-3, 4, -6] Point A [1,5,-3] point B[3,6,9]
X= [3-1, 6-5, 9-(-3)]
V = [2, 1, 12]
This helped
Soy
b) R=U*V
R=
V = [2,1, 12]
J = 2₁ + J + 12K (Unit vector notation)
11=4
k
-6
-3
2 1
R = 1(48+6)-3(-36 +12) + K (-3-8)
12
211-542 + 176 = 41
d)
(ordered pair notation) (using part 6)
Verifying
03613
CA
Let id=541 241-118
J (54)² + (24)² + (-11) ²
#547+242-11k
J2916 +376 +121
J3613
(54²₁ +243-11k)
- 3 5+243 -
K
$3613 J3613 √3613
n is orthogonal to t
n• U² = [34, 24, -11], C-3, 4, -6]
= -162 +96 +66
=0
Verifying in is orthogonal to
R·D= [54, 24, -11]. [2/1, 12]
105 +24-B2
= 0
e) Tlanc contains (2, 44, 7)
normal (n) [54,24,-117
Vector Equation
[R³-(21-431 7k)]. [54^1 +245 -11R]=0
Pargimetric, equations
J=[-3,4,-6]
V=[2,1, 12]
X=2=3€1+ 26₂
y=-4 +4+2+€₂
2-7-66₁ + 12 €₂
Seglar Equation
54 (x-2) + 24 (y + 4) - 11 (z-7)=0
54x + 24y - 112 + 65 =6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1aaa18f-7b3d-4067-9412-71bc31d5205a%2Fd2c0ae5d-bc57-4574-a900-88cae0f42a18%2Fb4jk8ob_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Criven that. I [-3, 4, -6] Point A [1,5,-3] point B[3,6,9]
X= [3-1, 6-5, 9-(-3)]
V = [2, 1, 12]
This helped
Soy
b) R=U*V
R=
V = [2,1, 12]
J = 2₁ + J + 12K (Unit vector notation)
11=4
k
-6
-3
2 1
R = 1(48+6)-3(-36 +12) + K (-3-8)
12
211-542 + 176 = 41
d)
(ordered pair notation) (using part 6)
Verifying
03613
CA
Let id=541 241-118
J (54)² + (24)² + (-11) ²
#547+242-11k
J2916 +376 +121
J3613
(54²₁ +243-11k)
- 3 5+243 -
K
$3613 J3613 √3613
n is orthogonal to t
n• U² = [34, 24, -11], C-3, 4, -6]
= -162 +96 +66
=0
Verifying in is orthogonal to
R·D= [54, 24, -11]. [2/1, 12]
105 +24-B2
= 0
e) Tlanc contains (2, 44, 7)
normal (n) [54,24,-117
Vector Equation
[R³-(21-431 7k)]. [54^1 +245 -11R]=0
Pargimetric, equations
J=[-3,4,-6]
V=[2,1, 12]
X=2=3€1+ 26₂
y=-4 +4+2+€₂
2-7-66₁ + 12 €₂
Seglar Equation
54 (x-2) + 24 (y + 4) - 11 (z-7)=0
54x + 24y - 112 + 65 =6
Transcribed Image Text:Suppose vector i = [-3,4,-6) and originates at point A at (1,5,-3) and terminates at point B at (3,6,9)
a. Find vector and write it in both ordered pair and unit vector notation
b. Find a normal to vectors and
c. Find a unit vector that is the same magnitude as the normal you obtained in question 2, part b.
Use the dot product to verify that the normal you obtained in question 2, part b is orthogonal to
both vectors and
d.
e. Suppose vectors and are both direction vectors in a plane that also contains the point
(2,-4,7). Determine:
L
A vector equation for the plane
Parametric equations for the plane
A scalar equation for the plane
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