Find the cosine of the angle between the normals to the planes

In summary, to find the cosine of the angle between the normals to the planes x+y+2z=3 and 2x-y+2z=5, you need to find the vectors that are normal to each plane. This can be done by following the steps outlined in the link provided, and then using the formula cos θ= V * W / ||V|| ||W|| to calculate the cosine of the angle between the two normals.
  • #1
whig4life
14
0
1. Homework Statement

Find the cosine of the angle between the normals to the planes:

x+y+2z=3 and 2x-y+2z=5

2. Homework Equations [/b]

x+y+2z=3 and 2x-y+2z=5

3. The Attempt at a Solution

All I know is cos θ= V * W / ||V|| ||W||
 
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  • #2
whig4life said:
1. Homework Statement

Find the cosine of the angle between the normals to the planes:

x+y+2z=3 and 2x-y+2z=5

2. Homework Equations [/b]

x+y+2z=3 and 2x-y+2z=5

3. The Attempt at a Solution

All I know is cos θ= V * W / ||V|| ||W||

The first step is to find the vectors that are normal to the planes. If you don't know how to do that try and look it up.
 
  • #3

FAQ: Find the cosine of the angle between the normals to the planes

What is the formula for finding the cosine of the angle between the normals to the planes?

The formula for finding the cosine of the angle between the normals to the planes is cosθ = (n1⋅n2) / (|n1|⋅|n2|), where n1 and n2 are the normal vectors to the two planes.

How do you find the normal vector to a plane?

The normal vector to a plane can be found by taking the cross product of two non-parallel vectors that lie on the plane. Another method is to use the coefficients of the plane's equation to determine the normal vector.

Can the angle between the normals to the planes be greater than 90 degrees?

No, the angle between the normals to the planes cannot be greater than 90 degrees. The cosine of an angle between two vectors is always between -1 and 1, so if the angle is greater than 90 degrees, the cosine would be negative.

What does the angle between the normals to the planes represent?

The angle between the normals to the planes represents the measure of the inclination between the two planes. It can also be thought of as the measure of the tilt or slope of the planes in relation to each other.

Can the angle between the normals to the planes be used to determine if the planes are parallel or perpendicular?

Yes, the angle between the normals to the planes can be used to determine if the planes are parallel or perpendicular. If the angle is 0 degrees, the planes are parallel. If the angle is 90 degrees, the planes are perpendicular. Any other angle would indicate that the planes are neither parallel nor perpendicular.

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