Question

The angle between two diagonals of a cube is

• A. $30^\circ$
• B. $45^\circ$
• C. $\cos^{-1} \left(\frac{1}{3} \right)$
• D. $\cos^{-1} \left( \frac{1}{\sqrt{3}} \right)$

Answer 1

Answer: (C)

$\cos^{-1} \left(\frac{1}{3} \right)$

Answer 2

The correct answer is Option C) $\cos^{-1} \left(\frac{1}{3} \right)$

O(0, 0, 0), A(a, 0, 0), B(0, a, 0), R(0, 0, a), D(a, a, 0), K(a, 0, a), L(0, a, a,), P(a, a, a) direction-cosines of diagonal Op is proportional to (a, a, a)

so, Op's direct cosines are:

The angle between two diagonals of a cube is cos–11/3.

Discover More Topics From This Chapter:Three-Dimensional Geometry