Under which one of the following conditions are the lines x = ay + b; z = cy + d and x = ey + f; z = gy + h perpendicular?

Question

Question

This question was previously asked in

NDA (Held On: 23 April 2017) Maths Previous Year paper

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Answer 1

Concept:

If two lines are perpendicular to each other’s then product of direction ratio of these lines is zero.

Calculation:

Given lines are x = ay + b and z = cy + d

⇒ x – b = ay and z – d = cy

…. (1)

Direction ration of line is (a, 1, c)

Again, Lines are x = ey + f and z = gy + h

⇒ x – f = ey and z – h = gy

…. (2)

Direction ration of line is (e, 1, g)

Given both line are perpendicular

∴ (a × e) + (1 × 1) + (c × g) = 0

⇒ ae + 1 + cg = 0

Or, ae + cg + 1 = 0