Question

The projection of the line segment joining the points $(-1,0,3)$ and $(2,5,1)$ on the line whose direction ratios are $6,2,3$ is

• A. $\frac{10}{7}$
• B. $\frac{22}{7}$
• C. $\frac{18}{7}$
• D. none of these

Answer 1

The correct option is B

$\frac{22}{7}$

Explanation for the correct option:

Find the projections of the line segment

Projection formula of the line joining points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ on the line whose direction ratios are $l,m,n$ is $(x_2-x_1)\frac{l}{\sqrt{l^2+m^2+n^2}}+(y_2-y_1)\frac{m}{\sqrt{l^2+m^2+n^2}}+(z_2-z_1)\frac{n}{\sqrt{l^2+m^2+n^2}}$

Projection of the line joining points $(-1,0,3)$ and $(2,5,1)$ on the line whose direction ratios are $6,2,3$ is

$$\begin{gathered} =(2+1)\frac{6}{\sqrt{6^2+2^2+3^2}}+(5-0)\frac{2}{\sqrt{6^2+2^2+3^2}}+(1-3)\frac{3}{\sqrt{6^2+2^2+3^2}} \\ =\left(3\right)\frac{6}{7}+\left(5\right)\frac{2}{7}+(-2)\frac{3}{7} \\ =\frac{18+10-6}{7} \\ =\frac{22}{7} \end{gathered}$$

Hence, option (B), $\frac{22}{7}$ is correct answer