Find the angle between the planes x + y + z = 1 and x - 2y + 3z = 1.

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AAI ATC Junior Executive 27 July 2022 Shift 3 Official Paper
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Answer (Detailed Solution Below)

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Detailed Solution

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Concept: 

The angle between the two planes A1x + B1y + C1z + D1 = 0 and A2x + B2y + C2z + D2 = 0 is

i.e. 

Calculation: 

Given: The planes x + y + z = 1 and x - 2y + 3z = 1.

Here  A1 = 1,  B1 = 1 C1 = 1 and A2 = 1, B2 = -2 C2 = 3

∴ The angle between the two planes x + y + z = 1 and x - 2y + 3z = 1.is

 ⇒  ⇒ 

∴ The angle between the planes is  .

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