Equations of Lines and Planes

Practice Questions

Calculus 3 › Equations of Lines and Planes

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1

Write down the equation of the line in vector form that passes through the points , and .

2

Determine the equation of the plane given by the following two vectors and the point :

$\left \langle 3, 1, 5\right \rangle, \left \langle 2, 1, 1\right \rangle$

3

Find the approximate angle between the planes , and .

4

Determine the equation of the plane containing the three points

5

Find the unit tangent vector given by the curve

$\vec{r}(t)=(te^t)\hat{i}+t^2\hat{j}+t^3\hat{k}$

6

Find the unit tangent vector to the curve given by

$\vec{r}(t)=3t\hat{i}+e^t\hat{j}+t^3\hat{k}$

7

Find the angle (in degrees) between the planes ,

8

Find the equation of the plane that contains the point , and has a normal vector $n=\left \langle 3,2,5 \right \rangle$ .

9

Find the equation of the plane that contains the point $\left ( 3,-6,7\right )$ and has a normal vector $n=\left \langle 4,2,1\right \rangle$

10

Find the equation of the plane containing the points

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