Question

Find the angle between the planes 2x-y+z=6 and x+y+2z=7

Answer 1

please check attachment

Answer 2

Given:

Two planes

2x-y+z=6 ---(1)

x+y+2z=7 ----(2)

Compare above equations with

A1x+B1y+C1z=D1 and

A2x+B2y+C2z =D2, we get

A1= 2, B1 = -1 , C1 = 1 , D1=6

and

A2=1, B2=1, C2= 2, D2 = 7

We know that,

Angle between two planes

=$\boxed {cos\theta = | \frac{A_{1}A_{2}+B_{1}B_{2}+C_{1}C_{2}}{\sqrt{A_{1}^{2}+B_{1}^{2}+C_{1}^{2}}\cdot\sqrt{A_{2}^{2}+B_{2}^{2}+C_{2}^{2}}} |}$

${cos\theta = | \frac{2\times1+(-1)\times1+1\times2}{\sqrt{2^{2}+(-1)^{2}+1^{2}}\cdot\sqrt{1^{2}+1^{2}+2^{2}}}| }$

= |(2-1+2)/(√6×√6)|

= |3/6|

= 1/2

$cos\theta$=cos60°

$\theta = 60$

Now ,

Angle between two given planes = 60°

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