Q18 of 177 Page 24

If a vector makes angles α, β, γ with OX, OY and OZ respectively, then write the value of sin²α + sin²β + sin²γ.

The sum of squares of direction cosines of a vector is 1.

Let the angles made by vector be α, β, γ. Then, we get

cos²α+cos²β+cos²γ=1

using cos²θ=1-sin²θ, we get

(1-sin²α) +(1-sin²β) +(1-sin²γ) =1

Or, sin²α+sin²β+sin²γ=2

If are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then write the value of .

Write a unit vector making equal acute angles with a coordinates axes.

Write a vector of magnitude 12 units which makes 45° angle with X-axis, 60° angle with y-axis and an obtuse angle with Z-axis.

Write the length (magnitude) of a vector whose projections on the coordinate axes are 12, 3 and 4 units.

If a vector makes angles α, β, γ with OX, OY and OZ respectively, then write the value of sin2α + sin2β + sin2γ.