Question

The direction ratios of the line, given by the planes x - y + z - 5 = 0, x - 3y - 6 = 0 are

• A. (3, 1, -2)
• B. (2, -4, 1)
• C. (1,-1, 1)
• D. (0,2,1)

Answer 1

The correct option is A (3, 1, -2)

Given,

$x–y+z–5=0=x–3y–6$

$\Rightarrow x–y+z–5=0$

$x–3y–6=0$

$\Rightarrow x–y+z–5=0$ (1)

$x=3y+6$ (2)

From (1) and (2) we get,

$3y+6–y+z–5=0$

$2y+z+1=0$

$y=\frac{-z-1}{2}$

Also, $y=\frac{x-6}{3}$ From (2)

$\therefore \frac{x-6}{3}=y=\frac{-z-1}{2}$

So, the given equation can be re-written as

$\frac{x-6}{3}=\frac{y}{1}=\frac{z+1}{-2}$

Hence the direction ratios of the given line are proportional to $3,1,-2$