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. d. Use the dot product to verify that the normal you obtained in question 2, part b is orthogonal to both vectors i and 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
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. d. Use the dot product to verify that the normal you obtained in question 2, part b is orthogonal to both vectors i and 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
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 )
Image 1: The question
Image 2: My work
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
![Given that U: [-3, 4, -6] Point A [1, 5,-3] point B[3,6,9]
V = [ 3-1, 6-5, 9 +(-3)]
V = [2, 1, 12]
This helped
a) So, V₁ = [2, 1, 12],
J = 2₁ + J + 12^1 (unit vector notation) Verifying ʼn is orthogonal tou
R
b) n = √₂ x v
R=
A
J
ĴK
4
-3
2
77² = 1 (48 + 6)-Ĵ(-36 +12) + K (-3-8)
54₁ +24 ^j - 11 k
-6
1 12
1
d)
(ordered pair notation) (using part b)
c)
Let w = 541 + 241-11 K
J (54)² + (24)² + (-11) ²
= 541 + 24 7 - HK
√2916 +576 + 121
4
= 54 ↑ + 24 Ĵ-11 k
J3613
√3613
OR
(54î+24ĵ-11K)
34
54 7 + 24 J
03613 J3613
11
√3613
K
n⋅U = [54, 24, -11], (-3, 4, -6]
= -162 +96-66
= 0
Verifying
in is orthogonal to V
R⋅V = [54₁ 24₁ -11]. [2, 1, 12]
= 108 + 24 =132
=0
e) Planc contains (2, +4,7)
normal (n) = [54, 24, -11]
Vector Equation
[R-(21-4j+ 7^k)]. [54^₁ + 24 ²5 -11 K ] = 0
Parametric, equation
U= [-3₁4₁-6]
V = [2/1, 12]
x = 2-3 £1+ 2+₂
y = - 4 +4€₂+ €₂
2= 7 -6 €₁ + 12 € ₂
Scalar Equation
54 (x-2) ₁24 (y + 4) - 11 (2-7)= 0
54x + 24 y = 11² + 65 =0
(-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff53b1b3a-ce83-4673-9838-32a83916512b%2F6c25f7e6-5fdf-401e-b742-3be285797d38%2Fth0ygrs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given that U: [-3, 4, -6] Point A [1, 5,-3] point B[3,6,9]
V = [ 3-1, 6-5, 9 +(-3)]
V = [2, 1, 12]
This helped
a) So, V₁ = [2, 1, 12],
J = 2₁ + J + 12^1 (unit vector notation) Verifying ʼn is orthogonal tou
R
b) n = √₂ x v
R=
A
J
ĴK
4
-3
2
77² = 1 (48 + 6)-Ĵ(-36 +12) + K (-3-8)
54₁ +24 ^j - 11 k
-6
1 12
1
d)
(ordered pair notation) (using part b)
c)
Let w = 541 + 241-11 K
J (54)² + (24)² + (-11) ²
= 541 + 24 7 - HK
√2916 +576 + 121
4
= 54 ↑ + 24 Ĵ-11 k
J3613
√3613
OR
(54î+24ĵ-11K)
34
54 7 + 24 J
03613 J3613
11
√3613
K
n⋅U = [54, 24, -11], (-3, 4, -6]
= -162 +96-66
= 0
Verifying
in is orthogonal to V
R⋅V = [54₁ 24₁ -11]. [2, 1, 12]
= 108 + 24 =132
=0
e) Planc contains (2, +4,7)
normal (n) = [54, 24, -11]
Vector Equation
[R-(21-4j+ 7^k)]. [54^₁ + 24 ²5 -11 K ] = 0
Parametric, equation
U= [-3₁4₁-6]
V = [2/1, 12]
x = 2-3 £1+ 2+₂
y = - 4 +4€₂+ €₂
2= 7 -6 €₁ + 12 € ₂
Scalar Equation
54 (x-2) ₁24 (y + 4) - 11 (2-7)= 0
54x + 24 y = 11² + 65 =0
(-
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