The angle between the planes 2x + y + z = 7 and x - y + 2z = 9 is:

  1. 60°
  2. 120°
  3. 90°
  4. 30°

Answer (Detailed Solution Below)

Option 1 : 60°
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Detailed Solution

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Concept:

The acute angle θ between two planes a1x + b1y + c1z = d1 and a2x + b2y + c2z = d2 is given by the formula:

.

 

Calculation:

Given: 2x + y + z = 7 and x - y + 2z = 9.

That means,

a1 = 2, b1 = 1, c1 = 1 and a2 = 1, b2 = - 1, c2 = 2.

To Find: Angle between the planes

Using the above formula for angle θ:

⇒ θ = 60°.

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