Question

if $\overrightarrow{a}=3\hat{i}-5\hat{j},\overrightarrow{b}=6\hat{i}+3\hat{j}$ and $\overrightarrow{c}=\overrightarrow{a}\times \overrightarrow{b}$ then $\left|\overrightarrow{a}\right|:\left|\overrightarrow{b}\right|:\left|\overrightarrow{c}\right|$

• 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)

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

$\left|\overrightarrow{a}\right|=\sqrt{9+35}=\sqrt{34}$
$\left|\overrightarrow{b}\right|=\sqrt{36+9}=\sqrt{45}$
$\overrightarrow{c}=\overrightarrow{a}\times \overrightarrow{b}=\left|\right[\left[\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& -5& 0\\ 6& 3& 0\end{array}\right]]|=39k$
$\therefore \left|\overrightarrow{c}\right|=39$