Question

A line passes through the points $(6,-7,-1)$ and $(2,-3,1)$. The direction cosines of the line so directed that the angle made by it with the positive direction of x-axis is acute, is?

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

Answer 1

The correct option is A $\frac{2}{3},-\frac{2}{3},-\frac{1}{3}$

Consider the problem

Let $l,m,n$ are direction cosines of the given line.

then as it made an acute angle with $x-axis$,

Therefore, $l>0$

The line passes through $(6,-7,-1)$ and $(2,-3,1)$

Therefore, its direction ratios are

$6-2,-7+3,-1-1$ or $2,-2,-1$

Hence direction cosines of the line are given by $\frac{2}{3},-\frac{2}{3},-\frac{1}{3}$.