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Comprehension

Consider the following for the next two (2) items that follow :

Let the plane  pass through the point (2, 3, -6).

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

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  1. <3, 2, 1>
  2. <2, 3, 6>
  3. <6, 3, 2>
  4. <1, 2, 3>

Answer (Detailed Solution Below)

Option 1 : <3, 2, 1>
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Detailed Solution

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Concept:

The equation to the plane passing through P(x1, y1, z1) and having direction ratios (a, b, c) for its normal is

a(x - x1) + b(y - y1) + c (z - z1) = 0.

Calculation:

Since the plane  pass through the point (2, 3, -6);

it satisfies the given equation.

⇒ 

⇒ k = 2

The given equation of the plane is 

Putting the value of k = 2, we get,

⇒ 3x + 2y + z = 6

The direction ratios of normal to the plane are <3, 2, 1>

∴ The direction ratios of normal to the plane are <3, 2, 1>

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