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(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

(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
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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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=
Transcribed Image Text:(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
Transcribed Image Text:(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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