Problem 6. Consider the plane, X, in R given by the vector equation: x(s, t) = (1, –1,2) + s(1,0, 1) + t(1, – 1,0); s, t e R. (a) Compute a unit normal vector, n, to this plane. (b) Define a linear transformation P: R³ → R³ by projection onto n: P(x) := proj,(x), x € R°. Compute the standard matrix, A, of P.
Problem 6. Consider the plane, X, in R given by the vector equation: x(s, t) = (1, –1,2) + s(1,0, 1) + t(1, – 1,0); s, t e R. (a) Compute a unit normal vector, n, to this plane. (b) Define a linear transformation P: R³ → R³ by projection onto n: P(x) := proj,(x), x € R°. Compute the standard matrix, A, of P.
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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Transcribed Image Text:Problem 6. Consider the plane, X, in R³ given by the vector equation:
x(s, t) = (1, – 1, 2) + s(1,0, 1) + t(1, –1,0);
s, t E R.
S
S
|
|
(a) Compute a unit normal vector, n, to this plane.
3
(b) Define a linear transformation P : R³ → R³ by projection onto n:
P(x) := proj,(x), x€ R.
X E
Compute the standard matrix, A, of P.
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Follow-up Question
why you write:
s=0, t=0
s=1, t=1
instead of using cross product imediately between 2 vectors (1,0,1) and (1,-1,0)
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