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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
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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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.
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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