Question

The projection of the line segment joining $(0,0,0)$ and $(5,2,4)$ on the line whose direction ratios are $2,-3,6$ is

• A. $28$
• B. $4$
• C. $\frac{40}{7}$
• D. $\sqrt{45}$

Answer 1

The correct option is B $4$

The line segment passing through the points $(0,0,0)$ and $(5,2,4)$ is parallel to $\overrightarrow{a}=5i+2j+4k$. The dr's of the line (as given ) is $\overrightarrow{l}=2i-3j+6k$
Hence the required projection is
$=\frac{\overrightarrow{a}.\overrightarrow{l}}{|\overrightarrow{l}|}$
$=\frac{10-6+24}{\sqrt{4+36+9}}$
$=\frac{28}{7}$
$=4$.