Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoordinates of a point in space, Direction cosines,Medium2 minPYQ_2016

MathematicsMediumsingle choice

The cosine of the angle between any two diagonals of a cube is

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Answer:

Solution:

Let the direction ratio's of two diagonals of a cube are (1,1,1) and (-1,1,1) $∴ cos θ = \frac{a _{1} a _{2} + b _{1} b _{2} + c _{f} c _{2}}{a _{1}^{2} + b _{1}^{2} + c _{1}^{2} a _{2}^{2} + b _{2}^{2} + c _{2}^{2}} = \frac{( 1 ) \times ( - 1 ) + ( 1 ) \times ( 1 ) + ( 1 ) \times ( 1 )}{( 1 ) ^{2} + ( 1 ) ^{2} + ( 1 ) ^{2} ( - 1 ) ^{2} + ( 1 ) ^{2} + ( 1 ) ^{2}} = \frac{- 1 + 1 + 1}{3 3} = \frac{1}{3}$

Stream:WBJEESubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Coordinates of a point in space, Direction cosines,

⏱ 2mℹ️ Source: PYQ_2016

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