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KCET 2014 Math Solved Paper

Question : 25 of 60

Marks: +1, -0

The angle between two diagonals of a cube is

Solution:

Let edge of the cube is 1 unit.

So, Angle between diagonals = Angle between The diagonals of the cube are

OA

and

BC

The DR's of diagonal OA are

(1,1,1)

and for

B C

are

(-1,1,1)

. The angle between the diagonals is given by,

\cos \theta \;=\; \frac{1(-1)+(1)(1)+1(1)}{\sqrt{1^2+1^2+1^2} \left( \sqrt{(-1)^2+1^2+1^2} \right)}

\;=\; \frac{1}{\sqrt{3} \left( \sqrt{3} \right)}

\;=\; \frac{1}{3}

\theta \;=\; \cos^{-1} \left( \frac{1}{3} \right)

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