## 17Calculus - Vector Lines-Planes Application - Normals & Tangent Planes

Using Vectors

Applications

### Partial Integrals

Double Integrals - 2Int

Triple Integrals - 3Int

Practice

### Articles

We will be adding more discussion here soon. In the meantime, enjoy these practice problems.

Practice

Find the equation of the tangent plane and the symmetric equations of the normal line to the surface $$2(x-2)^2 + (y-1)^2 + (x-3)^2 = 10$$ at the point $$(3,3,5)$$.

Problem Statement

Find the equation of the tangent plane and the symmetric equations of the normal line to the surface $$2(x-2)^2 + (y-1)^2 + (x-3)^2 = 10$$ at the point $$(3,3,5)$$.

Solution

### 1482 video

video by Krista King Math

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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

### 1767 video

video by Dr Chris Tisdell

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Determine a normal vector and the equation of the tangent plane to the surface $$z = x^2 + 2y^2$$ at the point $$A(2,-1,6)$$.

Problem Statement

Determine a normal vector and the equation of the tangent plane to the surface $$z = x^2 + 2y^2$$ at the point $$A(2,-1,6)$$.

Solution

### 1828 video

video by Dr Chris Tisdell

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Find the tangent plane to the surface $$x=u^2, y=u-v^2, z=v^2$$ for $$u,v \geq 0$$ at the point $$(1,0,1)$$.

Problem Statement

Find the tangent plane to the surface $$x=u^2, y=u-v^2, z=v^2$$ for $$u,v \geq 0$$ at the point $$(1,0,1)$$.

Solution

### 2529 video

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