Question

The projection of $\overrightarrow{a}=2\stackrel{\wedge }{i}+3\stackrel{\wedge }{j}-2\stackrel{\wedge }{k}$ on $\overrightarrow{b}=\stackrel{\wedge }{i}+2\stackrel{\wedge }{j}+3\stackrel{\wedge }{k}$ is:

• A. $\frac{1}{\sqrt{14}}$
• B. $\frac{2}{\sqrt{14}}$
• C. $\frac{-1}{\sqrt{14}}$
• D. $\frac{-2}{\sqrt{14}}$

Answer 1

Answer: (B)

$\frac{2}{\sqrt{14}}$

Projection of $\overrightarrow{a}=2\stackrel{\wedge }{i}+3\stackrel{\wedge }{j}-2\stackrel{\wedge }{k}$ on $\overrightarrow{b}=\stackrel{\wedge }{i}+2\stackrel{\wedge }{j}+3\stackrel{\wedge }{k}$ is

$=\frac{\overrightarrow{a}\cdot \overrightarrow{b}}{|\overrightarrow{b}|}=\frac{2}{\sqrt{14}}$