If x=3 i-6 j- k, y= i+4 j-3 k and z=3 i-4 j-12 k, then the magnitude of the projection of …

Question

If $\vec x=3\hat i-6\hat j-\hat k$, $\vec y=\hat i+4\hat j-3\hat k$ and $\vec z=3\hat i-4\hat j-12\hat k$, then the magnitude of the projection of $\vec x	imes\vec y$ on $\vec z$ is:

Accepted Answer

$$\vec x\times\vec y = \begin{vmatrix}\hat i&\hat j&\hat k\3&-6&-1\1&4&-3\end{vmatrix} = 22\hat i+8\hat j+18\hat k$$

$$\text{Projection on }\vec z = \frac{(\vec x\times\vec y)\cdot\vec z}{|\vec z|} = \frac{22(3)+8(-4)+18(-12)}{\sqrt{9+16+144}} = \frac{-182}{13}=-14$$

Magnitude of projection $=14$.

Solutions · 1