If p, q and r are the intercepts made by the plane on the coordinate axes respectively, then what is (p + q + r) equal to ?

Question

Question

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

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

This question was previously asked in

NDA 01/2022: Maths Previous Year paper (Held On 10 April 2022)

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Answer 1

Concept:

The equation of the plane whose intercepts are a, b, c on the x, y, z axes, respectively, is

(a, b, c ≠ 0)

Calculation:

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

So, it satisfies the given equation.

So,

⇒ k = 2

The given equation of the plane is

Putting the value of k = 2, we get,

⇒ 3x + 2y + z = 6

The equation of the plane in intercepts form,

⇒

2, 3, and 6 are the intercepts made by the plane on the coordinate axes, respectively.

So, Sum of the intercept = 2 + 3 + 6 = 11.

∴ The value of (p + q + r) is 11.

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