Question

A line passes through the points (6, –7, –1) and (2, –3, 1). The direction cosines of the line so directed that the angle made by it with positive direction of x-axis is acute, are ______.

विकल्प

• `2/3, (-2)/3, (-1)/3`

• `2/3, (-2)/3, 1/3`

• `2/3, 2/3, 1/3`

• `-2/3, 2/3, 1/3`

Answer 1

A line passes through the points (6, –7, –1) and (2, –3, 1). The direction cosines of the line so directed that the angle made by it with positive direction of x-axis is acute, are `underlinebb(2/3, (-2)/3, (-1)/3)`.

Explanation:

Direction ratios = x₂ – x₁, y₂ – y₁, z₂ – z₁

= (–4, 4, 2) or (+4, –4, –2)

⇒ (–2, 2, 1) or (2, –2, –1)

But (2)² + (–2)² + (–1)² = 9

Direction cosines = `2/3, -2/3, -1/3` or `-2/3, 2/3, 1/3`

But line make acute angle with positive direction of x-axis so ℓ = cosα is positive

⇒ direction cosines = `2/3, -2/3, -1/3`