Multiple Choice Questions

What are the direction ratios of a normal to the plane ........

Mathematics (NDA) Coordinate Geometry

Consider the following for the next two (02) items that follow :
Let the plane 2x/k+ 2y/3 +z/3 = 2 pass through the point (2, 3, -6).

What are the direction ratios of a normal to the plane ?

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2022 NDA -1 Math

<3, 2, 1>

<2, 3,6>

<6, 3, 2>

<1, 2, 3>

- The equation of the plane is given as $\frac{2 x}{k} + \frac{2 y}{3} + \frac{z}{3} = 2$ .

- To find the correct equation of the plane, substitute the point $(2, 3, - 6)$ into the equation:

- $\frac{2 (2)}{k} + \frac{2 (3)}{3} + \frac{- 6}{3} = 2$ .

- This simplifies to $\frac{4}{k} + 2 - 2 = 2$ , so $\frac{4}{k} = 2$ .

- Solving, $k = 2$ .

- The normal to the plane has direction ratios given by the coefficients in front of x, y, and z.

- Replacing k in the equation, the direction ratios are <6, 2, 1>.

- Correct Answer: Option 3: <6, 3, 2>

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