Question

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

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

Answer 1

The correct option is A $\sqrt{34}:\sqrt{45}:39$

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

$|\overrightarrow{a}|=\sqrt{3^2+5^2}=\sqrt{34}$

$|\overrightarrow{b}|=\sqrt{36+9}=\sqrt{45}$

$|\overrightarrow{c}|=39$