Question

The direction ratios of the lines x - y + z - 5 = 0 = x - 3y - 6 are ______ 

Options

• 3, 1, -2

• 2, -4, 1

• ${\displaystyle \frac{3}{\sqrt{14}},\frac{1}{\sqrt{14}},\frac{-2}{\sqrt{14}}}$

• ${\displaystyle \frac{2}{\sqrt{41}},\frac{-4}{\sqrt{41}},\frac{1}{\sqrt{41}}}$

Answer 1

The direction ratios of the lines x - y + z - 5 = 0 = x - 3y - 6 are 3, 1, -2.

Explanation:

Let a, b, c be the direction ratios of the line.

∴ a - b + c = 0 and .............(i)

a - 3b = 0 ..................(ii)

∴ ${\displaystyle \frac{a}{3}=\frac{b}{2}=\frac{c}{-2}}$

∴ the direction ratios of the line are 3, 1, -2.