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The angle between any two diagonals of a cube is ${Cos}^{- 1} \frac{1}{t}$ . Then value of $t^{t}$ is

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Correct option is C

Two diagonals OP and CSOP→ direction ratios are 1,1,1CS⇀ direction ratios are 1,1,-1if θ is the angle between two diagonals OP and CS thencosθ=1.1+1.1+1112+12+12.12+12+−12 =1+1+133 =13⇒ θ=cos−113it gives t=3⇒tt=33=27

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The angle between any two diagonals of a cube is Cos−11t. Then value of tt is

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The angle between any two diagonals of a cube is ${Cos}^{- 1} \frac{1}{t}$ . Then value of $t^{t}$ is