Given-vectors-x-3i-6j-k-y-i-4j-3k-and-z-3i-4j-12k-then-the-projection-of-X-Y-on-vector-Z-is-

Question Number 81629 by zainal tanjung last updated on 14/Feb/20

Given vectors x = 3 i - 6 j - k, y = i + 4 j - 3 k

and z = 3 i - 4 j + 12 k, then the projection

of X \times Y on vector Z is

Answered by mr W last updated on 14/Feb/20

X \times Y = | \begin{matrix} i & j & k \\ 3 & - 6 & - 1 \\ 1 & 4 & - 3 \end{matrix} | = 22 i + 8 j + 18 k

(X \times Y) \cdot Z = 22 \times 3 + 8 \times (- 4) + 18 \times 12 = 250

\frac{250}{3^{2} + {(- 4)}^{2} + 12^{2}} = \frac{250}{169}

p r o j e c t i o n X \times Y o n Z = \frac{250}{169} (3 i - 4 j + 12 k)

= \frac{750}{169} i - \frac{1000}{169} j + \frac{3000}{169} k

Commented by Zainal Arifin last updated on 14/Feb/20

Thanks sir . .