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AP EAMCET2011MathematicsThree Dimensional Geometry

The magnitude of the projection of the vector a =4 i -3 j +2 k on the line which makes equal angles with the coordinate axes is

Options

  1. A2
  2. B3
  3. C1 3
  4. D1 2

Correct answer

B. 3

Step-by-step solution

Let the vector v make an angle with each of the three axes, then direction cosine of v are Also, ^2 + ^2 + ^2 =1 Hence, direction cosine of v are or So, the required line which makes equal angle with the coordinate axes is v = 1 3 i 1 3 j 1 3 k Now, the magnitude of the projection of the vector a =4 i -3 j +2 j on line v . Projection of a along r aligned v & = a v | v | & = 3 / 3 1 = 3 aligned

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