Question

If the projection of $b$ on $a$ is twice the projection of $a$ on $b$, then $\left|b\right|$ -$\left|a\right|$ is equal to

• A. $|a-b|$
• B. $|a|+|b|$
• C. $|b|$
• D. $|a|$
• E. 1

Answer 1

Answer: (D)

Given,
projection of $b$ on $a=2$ projection of $a$ on $b$
$\therefore \frac{b\cdot a}{|a|}=\frac{2a\cdot b}{|b|}$
$\Rightarrow |b|=2|a|$
$\therefore |b|-|a|=2|a|-|a|$
$=|a|$