Find the cosine of the angle between the planes −1x+3y+1z=0 and the plane 5x+5y+4z=−4

The he cosine of the angle between the planes is .

Step-by-step explanation:

Using the definition of the dot product:

The given planes are

The angle between two normal vectors of the planes is the same as one of

the angles between the planes. We can find a normal vector to each of the

planes by looking at the coefficients of x, y, z.

The cosine of the angle between the planes

Therefore the cosine of the angle between the planes is .