Question

A line passes through the points $(6,-7,-1)$ and $(2,-3,1)$. If the angle a which the line makes with the positive direction of x-axis is acute, the direction cosines of the line are.

• A. $\left(2/3\right),(-2/3),(-1/3)$
• B. $\left(2/3\right),\left(2/3\right),(-1/3)$
• C. $\left(2/3\right),(-7/3),\left(1/3\right)$
• D. $\left(8/3\right),\left(2/3\right),\left(1/3\right)$

Answer 1

The correct option is A $\left(2/3\right),(-2/3),(-1/3)$

Direction Ratios of line joining $(6,-7,-1)$ and $(2,-3,1)$ are

$\to (6,-2,-7-(-3)-(-1\left)\right)$

$\to (4,-4,-2)$

if it make acute angle with positive x-axis then $D.R\left(x\right)>0$

D.C are $(\frac{4}{\sqrt{4^2+4^2+2^2}},\frac{-4}{4^2+4^2+2^2},\frac{-2}{4^2+4^2+2^2})$

$(\frac{4}{6},\frac{-4}{6},\frac{-2}{6})$

$(\frac{2}{3},\frac{-2}{3},\frac{-1}{3})$

$A$ is correct.