Let a=2 i+ j-2 k and b= i+ j.

Question

Let $\vec a=2\hat i+\hat j-2\hat k$ and $\vec b=\hat i+\hat j$. Let $\vec c$ be a vector such that $|\vec c-\vec a|=3$, $|(\vec a	imes\vec b)	imes\vec c|=3$ and the angle between $\vec c$ and $\vec a	imes\vec b$ is $30^{\circ}$. Then $\vec a\cdot\vec c$ is equal to:

Accepted Answer

$|\vec a|=\sqrt{4+1+4}=3$, and $\vec a\times\vec b=2\hat i-2\hat j+\hat k$, so $|\vec a\times\vec b|=\sqrt{4+4+1}=3$.

$$|(\vec a\times\vec b)\times\vec c| = |\vec a\times\vec b||\vec c|\sin30^{\circ} \implies 3=3|\vec c|\cdot\frac12 \implies |\vec c|=2$$

Solutions · 1