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BITSAT2015MathematicsThree Dimensional GeometryActual

A line makes the same angle with each of the X and Z -axes. If the angle , which it makes with Y-axis, is such that ² =3 ² , then ² equals

Options

  1. A2 / 5
  2. B1 / 5
  3. C3 / 5
  4. D2 / 3

Correct answer

C. 3 / 5

Step-by-step solution

Let l, ~m and n be the direction cosines. Then, l= , m = , n = array l we have l²+m²+n²=1 ² + ² + ² =1 2 ² +1- ² =1 2 ² - ² =0 2 ² -3 ² =0 [ ² =3 ² 0( given ) ] ² =2 / 3 ² = 1 1+ ² = 1 1+2 / 3 = 3 5 array

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