Question

Direction cosines of the line $\frac{x+2}{2}=\frac{2y-5}{3},z=-1$ is

• A. $\frac{4}{5},\frac{3}{5},0$
• B. $\frac{3}{5},\frac{4}{5},\frac{1}{5}$
• C. $-\frac{3}{5},\frac{4}{5},0$
• D. $\frac{4}{5},-\frac{2}{5},\frac{1}{5}$

Answer 1

Answer: (A)

Given equation of line is
$\frac{x+2}{2}=\frac{2y-5}{3},z+1=0$
or $\frac{x+2}{2}=\frac{y-\frac{5}{2}}{\frac{3}{2}},z+1=0$
Hence, $DR$ of a line are $<2,\frac{3}{2},0>$
Now , $\sqrt{2^2+{\left(\frac{3}{2}\right)}^2+0}$
$=\sqrt{4+\frac{9}{4}}=\sqrt{\frac{25}{4}}=\frac{5}{2}$
$\therefore DC$ of a line are
$<\frac{2}{5/2},\frac{3/2}{5/2},0>$ or $<\frac{4}{5},\frac{3}{5},0>$