Question

If vector $\overrightarrow{a}=2\hat{i}-3\hat{j}+6\hat{k}$ and vector $\overrightarrow{b}=-2\hat{i}+2\hat{j}-\hat{k}$, then ratio of Projection of $\overrightarrow{a}$ on vector $\overrightarrow{b}$ to Projection of $\overrightarrow{b}$ on $\overrightarrow{a}$ is equal to

• A. $\frac{3}{7}$
• B. $\frac{7}{3}$
• C. $3$
• D. $7$

Answer 1

Answer: (B)

$\frac{7}{3}$

From the condition given we get

$=\frac{\frac{a.b}{|b|}}{\frac{b.a}{|a|}}$

Now we know that $a.b=b.a$ ...(by property of scalar/dot product of vectors).

Hence the above expression simplifies as
$\frac{|a|}{|b|}$

$=\frac{7}{3}$