Question

A vector $\vec{a}$ makes equal acute angles on the coordinate axis. Then the projection of vector $\vec{ b }=5 \hat{ i }+7 \hat{ j }-\hat{ k }$ on $\vec{ a }$ is

• A. $\frac{11}{15}$
• B. $\frac{11}{\sqrt{3}}$
• C. $\frac{4}{5}$
• D. $\frac{3}{5 \sqrt{3}}$

Answer 1

Answer: (B)

$\frac{11}{\sqrt{3}}$

Answer 2

$\overline{ a }=\hat{ i }+\hat{ j }+\hat{ k }$ $\frac{\overline{ b } \cdot \overline{ a }}{|\overline{ a }|}=\frac{5+7-1}{\sqrt{3}}$ $=\frac{11}{\sqrt{3}}$