First slide

Scalars and Vectors

Question

If a vector $\vec{P}$ making angles $α, β,$ and $γ$ respectively with the X, Y and Z axes respectively. Then $\sin^{2} α + \sin^{2} β + \sin^{2} γ =$

Easy

A

0
B

1
C

2
D

3

Solution

$\begin{array}{l} \sin^{2} α + \sin^{2} β + \sin γ \\ = 1 - \cos^{2} α + 1 - \cos^{2} β + 1 - \cos^{2} γ \\ = 3 - (\cos^{2} α + \cos^{2} β + \cos^{2} γ) = 3 - 1 = 2 \end{array}$

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