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Three Dimensional Geometry — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsThree Dimensional Geometry1 Mark
Question
A plane passing through (−1, 2, 3) and whose normal makes equal angle with the coordinate axes is:
  1. x + y + z + 4 = 0
  2. x − y + z + 4 = 0
  3. x + y + z − 4 = 0
  4. x + y + z = 0
✓

Answer

  1. x + y + z − 4 = 0

Solution:

Since normal makes equal angles with coordinate axis.

So, it intercept with all the axis will be same. So equation of plane will be 

$\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{a}}+\frac{\text{x}}{\text{a}}=1$

⇒ x + y + z = a

Now, it passes through (−1, 2, 3), so

−1 + 2 + 3 = a

⇒ a = 4

⇒ x + y + z − 4 = 0

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