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

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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

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
(-

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