Question

If $a=3\hat{j}-5\hat{j}$ and $b=6\hat{i}+3\hat{j}$ are two vectors and $c$ is a vector such that $c=a\times b$, then $\left|a\right|:\left|b\right|:\left|c\right|$ is equal to

• A. $\sqrt{34}:\sqrt{45}:\sqrt{39}$
• B. $\sqrt{34}:\sqrt{45}:39$
• C. $34:39:45$
• D. $39:35:34$

Answer 1

Answer: (B)

$\sqrt{34}:\sqrt{45}:39$

We have,
$a=3\hat{i}-5\hat{j};b=6\hat{i}+3\hat{j};c=a\times b$
$\Rightarrow a=3\hat{i}-5\hat{j};b=6\hat{i}+3\hat{j};c=39\hat{k}$
$\Rightarrow \left|a\right|=\sqrt{34},\left|b\right|=\sqrt{45},\left|c\right|=39$
Therefore, $\left|a\right|:\left|b\right|:\left|c\right|=\sqrt{34}:\sqrt{45}:39$