Question

a. Find the projection of u 21j+3k on y- -i+3j+2k. Hence resolve u into two vectors, one parallel to y and the other perpendicular to v. b. Resolve v into two vectors, one parallel to υ and the other perpendicular to u.

Answer 1

U bar = 2i^+ j^+ 3K^, v bar - i^+ 3j^+ 2k^Projection of u bar on v bar = u bar. V bar = (2i^+ j^+ 3k^) (- I + 3j^+ 2k^)/squareroot 19 1/squareroot 14 (- 2 + 3 6) = 7/squareroot 14 = 7 squareroot 14/14 = 1/2^squareroot 14 v bar = -I + 3y^+ 2k^/ squareroot 14 Now, W bar = squareroot 14/2 v bat = -1/2 + 3/2j^+ k^W_1 bar is parallel to v bar W bar = (2j^- 3k^) V bar w bar = (- i^+ 3j^+ 2k^) (2j^- 3k^) = 6 - 6 = 0 So, w bar is perpendicular to v bar now w var = 2j^- 3k^/squareroot 13 Projection of u bar on w bar = u bar w bar = (2i^+ j^+ 3k^) (2j^- 3k^)