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

1 Answer
Nov 4, 2016

The angle is 105.1º

Explanation:

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 sqrt(4+25+1)=sqrt30
The modulus of vector2 is sqrt(9+4+36)=sqrt49=7
The costheta=-10/(7sqrt30)=-0.26
theta is the angle between the planes
:. theta=105.1º