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), and e) For the part c) would there are two answers I gotfor part e) I just want you to check if ai wrote the vector equation, parametric equation and scalar equaJust write the answers that are correct (e.g. a) correct, b) incorrect, etc)Image 1: The questionImage 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 notationb. Find a normal to vectors andc. 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 toboth vectors andd.e. Suppose vectors and are both direction vectors in a plane that also contains the point(2,-4,7). Determine:LA vector equation for the planeParametric equations for the planeA scalar equation for the plane QUESTION # 2:IGiven that ✓= [-3, 4, -6]This helpedb) nxJ = 2î + J + 12 ^ (unit vector notation) Verifying in is orthogonal to uLSo, V = [2,1, 12]R = 1[c) -4T1V = [ 3-1, 6-5, 9-(-3)]V = [2, 1, 12]جاع21² = 1 (48 + 6) - Ĵ(-36 +12) + ^ (-3-8)R² = 54₁ +245-11 R-6d)(ordered pair notation) [using part b)Let w = 541 + 243-11 kJ (54)² + (24)² + (-11) ²03613ORter=² 54î+ 2+5-11 KJ2916 +376 + 121=-=549 + 24 Ĵ²-11 KJ3613Point A [1/5,-3] point B [3,6,9](547 +245 -11K)5 4 7 4 2 4 3 - 11 R03613 J3613√3613n⋅U = [54, 24, -11], C-3, 4, -6]= -162 +96466= 0vVerifying in is orthogonal to|ñ· V = [54, 24, -11]. [2, 1, 12]= 105 + 24 = 132e) Planc contains (2, +4,7)normal (n) = [54, 24, -117Vector Equation[R-(2₁-4j+7^k)]. [54²^₁ +245 -11 K ] = 0Pargmetric, equaticsU= [-3₁4₁-6]V = [2₁1, 12]x = 2 = 3 £1 + 2t₂y = - 4 + 4 + 2 + £₂2= 7 -6€₁ + 12 € ₂Scolar Equation54 (x - 2) ₁ 24 (y + 4) - 11 (2-7) = 054x + 24 y = 11₂ + 65 = 6

Answered: Image /qna-images/answer/2575de8f-2f3f-44f5-b980-4c4b504c1b8c.jpg

Suppose vector i = [-3,4,-6) and originates at point A at (1,5,-3) and terminates at point B at (3 a. Find vector and write it in both ordered pair and unit vector notation b. Find a normal to vectors and d. c. Find a unit vector that is the same magnitude as the normal you obtained in question 2, Use the dot product to verify that the normal you obtained in question 2, part b is orthop both vectors and e. Suppose vectors and are both direction vectors in a plane that also contains the poin (2,-4,7). Determine: L A vector 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 a. Find vector and write it in both ordered pair and unit vector notation b. Find a normal to vectors and d. c. Find a unit vector that is the same magnitude as the normal you obtained in question 2, Use the dot product to verify that the normal you obtained in question 2, part b is orthop both vectors and e. Suppose vectors and are both direction vectors in a plane that also contains the poin (2,-4,7). Determine: L A vector 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), and e)

For the part c) would there are two answers I got

for part e) I just want you to check if ai wrote the vector equation, parametric equation and scalar equa

Just write the answers that are correct (e.g. a) correct, b) incorrect, etc)

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

QUESTION # 2:
I
Given that ✓= [-3, 4, -6]
This helped
b) n
x
J = 2î + J + 12 ^ (unit vector notation) Verifying in is orthogonal to u
L
So, V = [2,1, 12]
R = 1
[
c) -
4
T
1
V = [ 3-1, 6-5, 9-(-3)]
V = [2, 1, 12]
جاع
2
1² = 1 (48 + 6) - Ĵ(-36 +12) + ^ (-3-8)
R² = 54₁ +245-11 R
-6
d)
(ordered pair notation) [using part b)
Let w = 541 + 243-11 k
J (54)² + (24)² + (-11) ²
03613
OR
ter
=² 54î+ 2+5-11 K
J2916 +376 + 121
=-=549 + 24 Ĵ²-11 K
J3613
Point A [1/5,-3] point B [3,6,9]
(547 +245 -11K)
5 4 7 4 2 4 3 - 11 R
03613 J3613
√3613
n⋅U = [54, 24, -11], C-3, 4, -6]
= -162 +96466
= 0
v
Verifying in is orthogonal to
|ñ· V = [54, 24, -11]. [2, 1, 12]
= 105 + 24 = 132
e) Planc contains (2, +4,7)
normal (n) = [54, 24, -117
Vector Equation
[R-(2₁-4j+7^k)]. [54²^₁ +245 -11 K ] = 0
Pargmetric, equatics
U= [-3₁4₁-6]
V = [2₁1, 12]
x = 2 = 3 £1 + 2t₂
y = - 4 + 4 + 2 + £₂
2= 7 -6€₁ + 12 € ₂
Scolar Equation
54 (x - 2) ₁ 24 (y + 4) - 11 (2-7) = 0
54x + 24 y = 11₂ + 65 = 6

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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