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MHT CET202616 April 2026Evening ShiftMathematicsVector AlgebraActual

The equation of a line in cartesian form passing through (0, 0, 0) and (4, 3, c) and parallel to a b where a = 2 i + j + 2 k , b = 3 i - 4 j is

Options

  1. Ax-4 8 = y-3 6 = z + 11 2 11
  2. Bx-4 8 = y+3 6 = z + 11 2 -11
  3. Cx-4 8 = y-3 6 = z + 11 2 -11
  4. Dx+4 8 = y-3 6 = z + 11 2 -11

Correct answer

C. x-4 8 = y-3 6 = z + 11 2 -11

Step-by-step solution

The direction vector of the line is parallel to a b . a b = vmatrix i & j & k 2 & 1 & 2 3 & -4 & 0 vmatrix = i (0 - (-8)) - j (0 - 6) + k (-8 - 3) = 8 i + 6 j - 11 k The direction ratios of the line are proportional to 8, 6, -11 . The line passes through (0, 0, 0) and (4, 3, c) . Its direction ratios are 4 - 0, 3 - 0, c - 0 , which is 4, 3, c . Since the line is parallel to a b , the direction ratios must be proportional: 4 8 = 3 6 = c -11 1 2 = c -11 c = - 11 2 The line passes through the point (4, 3, c) = (4, 3,

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