Question

The projection of the line segment joining the points A(-1, 0, 3) and B(2, 5, 1) on the line whose direction ratios are proportional to 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 $\frac{22}{7}$

Given points of line segment

$A(-1,0,3)andB(2,5,1)$

direction ratio of line be $R(2+1,5-0,1-3)=R(3,5,-2)$

$a_1=3,b_1=5,c_1=-2$

$a_2=6,b_2=2,c_2=3$

projection of lines $l_{1}on{l}_2=\frac{a_1{a}_2+b_1{b}_2+c_1{c}_2}{\sqrt{a_2^2+b_2^2+c_2^2}}$

$\Rightarrow projection=\frac{3\times 6+5\times 2+3\times (-2)}{\sqrt{6^2+2^2+3^2}}$

$\Rightarrow projection=\frac{18+10-6}{\sqrt{36+4+9}}$

$\Rightarrow projection=\frac{22}{\sqrt{49}}$

$\Rightarrow projection=\frac{22}{7}$