Need help with part d, Markscheme is attatched alongside. I was going to ask that once you work out the vector that is orthogonal to A,B and C, how do you know that this same vector will then neccessarily be orthogonal to the plane? (a) Describe, in detail, the geometric object represented by the Carte-sian equation 3x - 5y + 2z = 0.(b) Describe, in detail, the geometric object represented by the para-metric equationsx = 1+2\y = 2+A2=3-Aand c =(c) Determine the intersection of the geometric objects in (a) and (b)above.2"(d) Find a vector perpendicular to the plane that passes through the12points A, B and C, with position vectors a =01112(6)3XER.respectively.b= (d) Let u and v be the free vectors represented by AB and AC.Since uxv is orthogonal to both u and v, then u xv is orthogonalto the plane through A, B, C.We compute that u = b - a=Hence u x V =-(0)-2(3)and v=c-a=is orthogonal to the plane.C02

Given that the position vectors of the points A , B and C are…

Answered: (d) Find a vector perpendicular to the…

(d) Find a vector perpendicular to the plane that passes through the 1 2 points A, B and C, with position vectors a = ).D - ( 1₁ b= and c = 2 (G 3 0 respectively. " 0

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

Need help with part d, Markscheme is attatched alongside. I was going to ask that once you work out the vector that is orthogonal to A,B and C, how do you know that this same vector will then neccessarily be orthogonal to the plane?

(a) Describe, in detail, the geometric object represented by the Carte-
sian equation 3x - 5y + 2z = 0.
(b) Describe, in detail, the geometric object represented by the para-
metric equations
x = 1+2\
y = 2+A
2=3-A
and c =
(c) Determine the intersection of the geometric objects in (a) and (b)
above.
2
"
(d) Find a vector perpendicular to the plane that passes through the
1
2
points A, B and C, with position vectors a =
0
1
1
1
2
(6)
3
XER.
respectively.
b=

(d) Let u and v be the free vectors represented by AB and AC.
Since uxv is orthogonal to both u and v, then u xv is orthogonal
to the plane through A, B, C.
We compute that u = b - a=
Hence u x V =
-(0)-
2
(3)
and v=c-a=
is orthogonal to the plane.
C
0
2

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