17Calculus - Vector Lines-Planes Application - Normal & Tangent Planes

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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

Dr Chris Tisdell - 1767 video 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

Steve Butler - 4320 video 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

Steve Butler - 4331 video solution

video by Steve Butler

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