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We will be adding more discussion here soon. In the meantime, enjoy these practice problems.
Practice
Determine the equation of the line that passes through the point \( (1,-1,1) \) and is normal to the plane \( 2x + 3y - z = 4 \).
Problem Statement
Determine the equation of the line that passes through the point \( (1,-1,1) \) and is normal to the plane \( 2x + 3y - z = 4 \).
Solution
video by Dr Chris Tisdell |
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Find the plane which contains the points \( (2,4,-1) \) and \( (1, 3, -1) \) and perpendicularly intersects with the plane \( 3x + 5y + 4x = 27 \).
Problem Statement
Find the plane which contains the points \( (2,4,-1) \) and \( (1, 3, -1) \) and perpendicularly intersects with the plane \( 3x + 5y + 4x = 27 \).
Solution
video by Steve Butler |
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Find the centers and radii of both spheres which satisfy the following: the sphere is tangent to the planes \(2x+y-2z=7\) and \(8x-4y+z=-24\), and the center of the sphere lies on the line \(x=2+t, y=3+2t, z=-3t\).
Problem Statement
Find the centers and radii of both spheres which satisfy the following: the sphere is tangent to the planes \(2x+y-2z=7\) and \(8x-4y+z=-24\), and the center of the sphere lies on the line \(x=2+t, y=3+2t, z=-3t\).
Solution
video by Steve Butler |
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