Find the angel between any two diagonals of a cube.

Options

A. `theta=30^@`
B. `theta=45^@`
C. `2costheta=1`
D. `3costheta=1`

Answer

D

Explanation

diagonals are OP and AD and A cute anngle `=theta`
`costheta=abs((a_1a_2+b_1b_2+c_1c_2)/(sqrt(a_1^2+b_1^2+c_1^2)sqrt(a_2^2+b_2^2+c_2^2)))`
`=abs((a(-a)+(a)(a) +(a) (a))/(sqrt(a^2+a^2+a^2)sqrt(a^2+a^2+a^2)))`
`=abs((-a^2+a^2+a^2)/(sqrt(3a^2)sqrt(3a^2)))=abs(a^2/(3a^2))=1/3`
`rArr 3costheta=1`