How many unit vectors are there for which cos⁡α=12 and cos⁡β=12,, where α and β are angles made with X-axis and Y-axis, respectively.

cos2⁡α+cos2⁡β+cos2⁡γ=1 or  14+14+cos2⁡γ=1 or  cos2⁡γ=1−12=12∴ cos⁡γ=±12Two values of cos γ are possible. Hence, two vectors are possible, one corresponding to direction cosines 12,12,12 and other corresponding to direction cosines 12,12−12