Question

Let x be the angle formed by the diagonal of the face of a cube and the diagonal of the cube, drawn from the same vertex. $co{s}^{2}x=$

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $\frac{3}{2}$
• E. $\frac{2}{3}$

Answer 1

The correct option is E $\frac{2}{3}$

• The length of diagonal of cube is $\sqrt{3}a$ and the length of diagonal of face of cube is $\sqrt{2}a$ ($a$ is side length of cube)
• We get $cosx=\sqrt{2}/\sqrt{3}$
• Which implies ${\cos }^{2}x=\frac{2}{3}$