Given the vectors u = (1, 1,-1,-1) and v = (2, -3, 0, 6), and the point x = (-1,0,2,1) in R¹. (i) Find (2u-v). (2u + v). (ii) Find the parametric equations of the plane that passes through the point x, and is parallel to both u and v. Use s and t as parameters. (iii) Find the vector component of v along u, and the vector component of v orthogonal to u.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Given the vectors u= (1,1, –1, –1) and v =
(2, –3,0, 6), and the point xo = (-1,0, 2, 1)
in R'.
(i) Find (2u – v) · (2u + v).
(ii) Find the parametric equations of the plane that passes through the point xo and is
parallel to both u and v. Use s and t as parameters.
(iii) Find the vector component of v along u, and the vector component of v orthogonal
to u.
Transcribed Image Text:Given the vectors u= (1,1, –1, –1) and v = (2, –3,0, 6), and the point xo = (-1,0, 2, 1) in R'. (i) Find (2u – v) · (2u + v). (ii) Find the parametric equations of the plane that passes through the point xo and is parallel to both u and v. Use s and t as parameters. (iii) Find the vector component of v along u, and the vector component of v orthogonal to u.
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