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AP EAMCET2016MathematicsThree Dimensional Geometry

If a line makes angles , , and with the four diagonals of a cube, then the value of ^2 + ^2 + ^2 + ^2 is

Options

  1. A4 3
  2. B8 3
  3. C7 3
  4. D5 3

Correct answer

B. 8 3

Step-by-step solution

Given that, line makes angles , , , with the four diagonals of a cube, then we know that aligned & ^2 + ^2 + ^2 + ^2 = 4 3 & Since, ^2 =1- ^2 & 1- ^2 +1- ^2 +1- ^2 +1- ^2 = 4 3 & ^2 + ^2 + ^2 + ^2 =4- 4 3 = 8 3 aligned

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