Question

Assertion (A): A line can have direction cosines < 1, 1, 1>

Reason (R): cos θ = 1 is possible for θ = 0.

विकल्प

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

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

Answer 1

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

Explanation:

Assertion (A) is False: Direction cosines l, m, n must satisfy the condition l² + m² + n² = 1. For the values (1, 1, 1), the sum of squares is 1² + 1² + 1² = 3 ≠ 1. Therefore, (1, 1, 1) cannot be the direction cosines of any line.

Reason (R) is True: The statement cosθ = 1 is true when θ = 0, which is a valid trigonometric property.