How do you find the angle between the planes 2 x + 5 y &#x2212;<!-- - --> z

Angel Malone

Angel Malone

Answered question

2022-05-22

How do you find the angle between the planes 2 x + 5 y z = 6 and 3 x 2 y + 6 z = 10 ?

Answer & Explanation

Danube2w

Danube2w

Beginner2022-05-23Added 7 answers

Step 1
You look for the angle between the vectors normal to the planes:
Plane1, the vector is 2 , 5 , - 1
Plane2, the vector is 3 , - 2 , 6
The dot product is 2 ,   5 ,   1 3 ,   2 ,   6 = 6 10 6 = 10
The modulus of vector1 is 4 + 25 + 1 = 30
The modulus of vector2 is 9 + 4 + 36 = 49 = 7
The cos θ = - 10 7 30 = - 0.26
θ is the angle between the planes
θ = 105.1 º

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