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MHT CET202619 April 2026Evening ShiftMathematicsThree Dimensional GeometryActual

If , , are the direction angles of the line x = 4z + 3 and y = 2 - 3z , then the value of + + is...

Options

  1. A8 26
  2. B6 26
  3. C4 26
  4. D2 26

Correct answer

D. 2 26

Step-by-step solution

The equations of the line are given as x = 4z + 3 and y = 2 - 3z . Rewriting these equations in symmetric form: x - 3 4 = z y - 2 -3 = z Combining them, we get: x - 3 4 = y - 2 -3 = z - 0 1 The direction ratios of the line are 4, -3, 1 . The direction cosines , , are given by dividing the direction ratios by their magnitude 4^2 + (-3)^2 + 1^2 = 16 + 9 + 1 = 26 . = 4 26 = -3 26 = 1 26 Summing these values: + + = 4 - 3 + 1 26 = 2 26 Answer: 2 26

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