a=3 i-5 j and b=6 i+3 j are two vectors, and c is a vector such that c= a b, then | a|:| b…

Question

$\vec a=3\hat i-5\hat j$ and $\vec b=6\hat i+3\hat j$ are two vectors, and $\vec c$ is a vector such that $\vec c=\vec a	imes\vec b$, then $|\vec a|:|\vec b|:|\vec c|$ is:

Accepted Answer

$$\vec a\times\vec b = \begin{vmatrix}\hat i&\hat j&\hat k\3&-5&0\6&3&0\end{vmatrix}=39\hat k=\vec c$$

$|\vec a|=\sqrt{34}$, $|\vec b|=\sqrt{45}$, $|\vec c|=39$, so $|\vec a|:|\vec b|:|\vec c|=\sqrt{34}:\sqrt{45}:39$

Solutions · 1