Question

The direction cosines of a line whose equations are $\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-2}{-3}$

• A. $\frac{1}{\sqrt{14}},\frac{-3}{\sqrt{14}},\frac{2}{\sqrt{14}}$
• B. $\frac{2}{\sqrt{29}},\frac{4}{\sqrt{29}},\frac{-3}{\sqrt{29}}$
• C. $\frac{1}{\sqrt{29}},\frac{-3}{\sqrt{29}},\frac{2}{\sqrt{29}}$
• D. $2,4,-3$

Answer 1

The correct option is B $\frac{2}{\sqrt{29}},\frac{4}{\sqrt{29}},\frac{-3}{\sqrt{29}}$

Step 1:

The direction ratios of the line joining these points are

$(x_2-x_1),(y_2-y_1),(z_2-z_1)$

$(i.e)2,4,-3$

$\therefore$ Direction cosines are

$\frac{2}{\sqrt{2^2+4^2+(-3{)}^2}},\frac{4}{\sqrt{2^2+4^2+(-3{)}^2}},\frac{-3}{\sqrt{2^2+4^2+(-3{)}^2}}$

$⟹\frac{2}{\sqrt{29}},\frac{4}{\sqrt{29}},\frac{-3}{\sqrt{29}}$