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Let u = (-5,-2, 4), v = (3,6,-5) and w (-7,1,-8). (a) Calculate (u x v). w and hence find the volume of the parallelepiped w adjacent sides u, v and w. (b) Using the given vectors above, show that (i) vectors (u-proj, u) and w are orthogonal. (ii) Ilv|l*||w\|? – (v.w)² = ||v x wll?. %3D

Let u = (-5,-2, 4), v = (3,6,-5) and w (-7,1,-8). (a) Calculate (u x v). w and hence find the volume of the parallelepiped w adjacent sides u, v and w. (b) Using the given vectors above, show that (i) vectors (u-proj, u) and w are orthogonal. (ii) Ilv|l*||w\|? – (v.w)² = ||v x wll?. %3D

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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8. Let u = (-5,–2,4), v = (3, 6, –5) and w = (-7,1,-8). (a) Calculate (u x v). w and hence find the volume of the parallelepiped with adjacent sides u, v and w. (b) Using the given vectors above, show that (i) vectors (u - projw u) and w are orthogonal. (ii) Ilv|l*||w\|? – (v. w)² = ||v x wl| . (ii) (u x v) x w = (u.w)v – (v.w)u . -
Transcribed Image Text:8. Let u = (-5,–2,4), v = (3, 6, –5) and w = (-7,1,-8). (a) Calculate (u x v). w and hence find the volume of the parallelepiped with adjacent sides u, v and w. (b) Using the given vectors above, show that (i) vectors (u - projw u) and w are orthogonal. (ii) Ilv|l*||w\|? – (v. w)² = ||v x wl| . (ii) (u x v) x w = (u.w)v – (v.w)u . -
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