(a) Find the vector Q=[0, a,0] such that the resultant of the vectors: P=[5, 7, 8], Q=[0, a, 0] , R= [0, 3, –3], S= [-6, 7,0] lies in the xz-plane. (b) Choose any two vectors a and b in the three dimensional space R and verify the identity 4 (a · b) = |a+ bl? – la – bl?. (c) Find value(s) of a so that the planes x + 2y + 3z = 6 and a+ ay + z = 0 are orthogonal.
(a) Find the vector Q=[0, a,0] such that the resultant of the vectors: P=[5, 7, 8], Q=[0, a, 0] , R= [0, 3, –3], S= [-6, 7,0] lies in the xz-plane. (b) Choose any two vectors a and b in the three dimensional space R and verify the identity 4 (a · b) = |a+ bl? – la – bl?. (c) Find value(s) of a so that the planes x + 2y + 3z = 6 and a+ ay + z = 0 are orthogonal.
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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