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(a) Find the value of p so that the vectors i+2j+k and i+j+ pk are perpendicular. Find the cosine of the angle between the vectors 2i+j+k and i-j-2k. Hence, find the length of projection of 2i+j+k on i-j-2k . (b) (c) If a = i+2j-k and b = j+k, find a unit vector perpendicular to both a and b.

(a) Find the value of p so that the vectors i+2j+k and i+j+ pk are perpendicular. Find the cosine of the angle between the vectors 2i+j+k and i-j-2k. Hence, find the length of projection of 2i+j+k on i-j-2k . (b) (c) If a = i+2j-k and b = j+k, find a unit vector perpendicular to both a and b.

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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(a) Find the value of p so that the vectors i+2j+k and i+j+pk are perpendicular. Find the cosine of the angle between the vectors 2i+j+k and i- j-2k . Hence, find the length of projection of 2i+ j+k on i-j-2k . (b) (c) If a = i+2j-k and b= j+k, find a unit vector perpendicular to both a and b. 1 (b) 6’ V6 3 1 (c) V11 [(a) p=-3 or
Transcribed Image Text:(a) Find the value of p so that the vectors i+2j+k and i+j+pk are perpendicular. Find the cosine of the angle between the vectors 2i+j+k and i- j-2k . Hence, find the length of projection of 2i+ j+k on i-j-2k . (b) (c) If a = i+2j-k and b= j+k, find a unit vector perpendicular to both a and b. 1 (b) 6’ V6 3 1 (c) V11 [(a) p=-3 or
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