Question

O is the centre, AB and AC are two diagonals of the adjacent faces of a rectangular box. If angles AOB, BOC and COA are $\theta ,\varphi ,\Psi$ respectively then cos $\theta +cos\varphi +cos\Psi$ is equal to

• A. 1
• B. 0
• C. -1
• D. $\frac{3}{2}$

Answer 1

The correct option is C

-1

Let O be origin and axes parallel to edges. Coordinates of A, B, C are A(a, -b, -c) B (a, b,c) c (-a, b, -c)

Hence cos $\theta +cos\varphi +cos\Psi$

$=\frac{(a^2-b^2-c^2)+(-a^2+b^2-c^2)+(-a^2-b^2+c^2)}{a^2+b^2+c^2}$

=-1