Question

The projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are ______.

विकल्प

• `6/5, (-3)/5, 2/5`

• `6/7, (-3)/7, 2/7`

• `(-6)/7, (-3)/7, 2/7`

• 6, –3, 2

Answer 1

The projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are `underlinebb(6/7, (-3)/7, 2/7)`.

Explanation:

Let P (x₁, y₁, z₁) and Q (x₂, y₂, z₂) be the initial and final points of the vector whose projections on the three coordinate axes are 6, –3, 2 then 

x₂ – x₁, = 6 ; y₂ – y₁ = – 3 ; z₂ – z₁ = 2

So that direction ratios of `vec(PQ)` are 6, –3, 2

∴ Direction cosines of `vec(PQ)` are 

`6/sqrt(6^2 + (-3)^2 + 2^2), (-3)/sqrt(6^2 + (-3)^2 + 2^2)`,

`2/sqrt(6^2 + (-3)^2 + 2^2) = 6/7, (-3)/7, 2/7`