Let a(3 i+12 j+2 k).

Question

Let $\vec a\perp\left(3\hat i+\dfrac12\hat j+2\hat kight)$. If $\vec a	imes(2\hat i+\hat k)=2\hat i-13\hat j-4\hat k$, the projection of $\vec a$ on $2\hat i+2\hat j+\hat k$ is:

Accepted Answer

Let $\vec a=(a_1,a_2,a_3)$. $\vec a\cdot\left(3,\dfrac12,2\right)=0$: $3a_1+\dfrac{a_2}2+2a_3=0$ \ldots  (i)

$\vec a\times(2,0,1) = (a_2,\ 2a_3-a_1,\ -2a_2) = (2,-13,-4)$: $a_2=2$ \ldots  (ii), $a_1-2a_3=13$ \ldots  (iii)

From (i),(iii): $a_1=3,\ a_3=-5$. So $\vec a = 3\hat i+2\hat j-5\hat k$.

$$\text{Projection on }(2,2,1) = \frac{6+4-5}3 = \frac53$$

Solutions · 1