Let a=3 i- j+2 k, b = a( i-2 k), c = b k.

Question

Let $\vec a=3\hat i-\hat j+2\hat k$, $\vec b = \vec a	imes(\hat i-2\hat k)$, $\vec c = \vec b	imes\hat k$. Then the projection of $(\vec c-2\hat j)$ on $\vec a$ is:

Accepted Answer

$$\vec b = \vec a\times(\hat i-2\hat k) = \begin{vmatrix}\hat i&\hat j&\hat k\3&-1&2\1&0&-2\end{vmatrix} = 2\hat i+8\hat j+\hat k$$
$$\vec c = \vec b\times\hat k = (2,8,1)\times(0,0,1) = (8,-2,0)$$
$$\vec c - 2\hat j = 8\hat i-4\hat j$$

$$\text{Projection on }\vec a = \frac{(8,-4,0)\cdot(3,-1,2)}{|\vec a|} = \frac{24+4+0}{\sqrt{14}} = \frac{28}{\sqrt{14}} = 2\sqrt{14}$$

Solutions · 1