VITEEE 2015 Paper

Let α, β and γ be the angles made by the line segment OP with X-axis, Y-axis and Z-axis, respectively.
Given , α =

π

4

and β =

π

3

We know that, cos2α+cos2β+cos2γ = 1
∴ cos2

π

4

+cos2

π

3

+cos2γ = 1
⇒ (

1

√2

)2+(

1

2

)2+cos2γ = 1
⇒

1

2

+

1

4

+cos2γ = 1
⇒ cos2 γ =

1

4

⇒ cos γ =

1

√2

∴ γ =

π

4

Hence, direction cosines are cos α, cos β, cos γ i.e.

1

√2

,

1

2

,

1

√2