Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryLine ( Equation etc.)Medium2 minQB

MathematicsMediummultiple choice

The equation of the line $x + y + z - 1 = 0, 4 x + y - 2 z + 2 = 0$ written in the symmetrical form is

Options:(select one or more)

Answer:

A, B, C

Solution:

The direction ratios are $(1, 1, 1) \times (4, 1, - 2) = (- 3, 6, - 3) \propto (1, - 2, 1)$ . Put $z = k$ : $x = k - 1, y = 2 - 2 k$ . Points $(- 1, 2, 0) (k = 0), (0, 0, 1) (k = 1)$ and $(- \frac{1}{2}, 1, \frac{1}{2}) (k = \frac{1}{2})$ lie on the line, so A, B and C are correct. D has direction ratios (2, -1, 2), which is not parallel.

Stream:JEESubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Line ( Equation etc.)

⏱ 2mℹ️ Source: QB

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