Question

The angle between any two diagonals of a cube is

• A. $co{s}^{-1}\frac{1}{\sqrt{3}}$
• B. $co{s}^{-1}\frac{2}{3}$
• C. $co{s}^{-1}\frac{1}{3}$
• D. $co{s}^{-1}\frac{3}{4}$

Answer 1

Answer: (C)

Direction ratios of $OP$ are $<a,a,a>$ or $<1,1,1>$
and those of $AL$ are $<-a,a,a>$ or $<-1,1,1>$
$\therefore \cos \theta =\frac{-1+1+1}{\sqrt{3}\cdot \sqrt{3}}=\frac{1}{3}$