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

Question

Let $\vec a=2\hat i+\hat j-2\hat k$, $\vec b=\hat i+\hat j$. If $\vec c$ is a vector such that $\vec a\cdot\vec c=|\vec c|$, $|\vec c-\vec a|=2\sqrt2$ and the angle between $\vec a	imes\vec b$ and $\vec c$ is $30^{\circ}$, then $|(\vec a	imes\vec b)	imes\vec c|$ equals:

Accepted Answer

$|\vec a|=3$, $\vec a\times\vec b=2\hat i-2\hat j+\hat k$, $|\vec a\times\vec b|=3$.

$$|(\vec a\times\vec b)\times\vec c| = |\vec a\times\vec b||\vec c|\sin30^{\circ} = 3\cdot1\cdot\frac12=\frac32$$

Solutions · 1