Question

Assertion (A): Lines given by x = py + q, z = ry + s and x = p′y + q′, z = r′y + s′ are perpendicular to each other when pp′ + rr′ = 1.

Reason (R): Two lines `vecr = veca_1 + lambda vecb_1 and vecr = veca_2 + mu vecb_2` are perpendicular to each other if `vecb_1 * vecb_2 = 0`.

Options

• Both Assertion (A) and Reason (R) are true, and the Reason (R) is the correct explanation of the Assertion (A).

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

• Assertion (A) is true, and Reason (R) is false.

• Assertion (A) is false, and Reason (R) is true.

Answer 1

Assertion (A) is false, and Reason (R) is true.

Explanation:

Direction ratios are (p, 1, r) and (p′ + 1 + r′).

For perpendicular lines,

pp′ + 1 + rr′ = 0

pp′ + rr′ = −1, not 1

Hence, the assertion is false and the reason `vecb_1 * vecb_2 = 0` is correct, so Reason is true.