Question

If $\overline{a}=3\acute{i}-5\acute{j},\overline{b}=6\acute{i}+3\acute{j}$ are two vectors and $\overline{c}$ is a vector such that $\overline{c}=\overline{a}\times \overline{b}$, then $\left|\begin{array}{c}\overline{a}\end{array}\right|:\left|\begin{array}{c}\overline{b}\end{array}\right|:\left|\begin{array}{c}\overline{c}\end{array}\right|=$

• 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)

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

Given $\overline{c}=\overline{a}\times \overline{b}$

$=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& -5& 0\\ 6& 3& 0\end{array}\right|$
$\therefore \overline{c}=39\hat{k}$

Now $\left|\overline{a}\right|=\sqrt{34},\left|\overline{b}\right|=\sqrt{45}$ and $\left|\overline{c}\right|=\left|39\hat{k}\right|=39$
$\therefore \left|\overline{a}\right|:\left|\overline{b}\right|:\left|\overline{c}\right|=\sqrt{34}:\sqrt{45}:\sqrt{39}$