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99 Percentile Qs Bank for JEE MainMathematicsThree Dimensional Geometry

If the line segment joining the points A ,   B makes projection 1 ,   4 ,   3 on X ,   Y and Z -axes, respectively. Then, the direction cosines of A B are

Options

  1. A1 ,   4 ,   3
  2. B1 26 ,   4 26 ,   3 26
  3. C- 1 26 ,   4 26 ,   3 26
  4. D1 26 ,   - 4 26 ,   3 26

Correct answer

B. 1 26 ,   4 26 ,   3 26

Step-by-step solution

The projection of the line segment on the axes are x = 1 ,   y = 4 and z = 3 . We know that r = x 2 + y 2 + z 2 ⇒   r = 1 2 + 4 2 + 3 2 ⇒   r = 1 + 16 + 9 r = 26 . Now, the direction cosines of the line segment are respectively l = x r ,   m = y r ,   n = z r , ⇒   l = 1 26 ,   m = 4 26 ,   n = 3 26 .

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