Question

Find the direction ratio Of vector perpendicular to the lines whose direction cosines are 1,3,2 and -1,1,2

Answer 1

Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6.

Answer 2

Let the direction ratios of vector perpendicular to both given lines are a,b and c.

∵ Required vector is perpendicular to the lines whose direction ratios are 1,3 & 2. and -1,1 & 2.

∴ a + 3b + 2c = 0 and

- a + b + 2c = 0

\(\frac{a}{3\times 2\,-1\times 2}\) = \(\frac{b}{2\times -1\,-\,2\times 1}\) = \(\frac{c}{1\times 1-(-1)\times 3}\) = λ (Let)

(By cross multiplication method)

\(\frac{a}{4}\) = \(\frac{b}{-4}\) = \(\frac{c}{4}\)

Hence,

The direction ratio of vector perpendicular to given lines are 4,-4 & 4.