Question

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.

Answer 1

Let the angles made by vector be α, β, γ and the magnitude be m.

Given that α = 45°, β = 60° and m = 12. We have to figure out the vector.

Since cos²α + cos²β + cos²γ = 1, we get

cos²45° + cos²60° + cos²γ = 1

Since γ is obtuse, cos γ = \(-\cfrac12\)

Any vector, if it’s magnitude and direction cosines are given can be written as

So the required vector is

Rationalizing, we get