# Multivariable Calculus : Matrices & Vectors

## Example Questions

### Example Question #1 : Multivariable Calculus

Find the equation of the tangent plane to  at .

Explanation:

First, we need to find the partial derivatives in respect to , and , and plug in .

Remember that the general equation for a tangent plane is as follows:

Now lets apply this to our problem

### Example Question #2 : Multivariable Calculus

Find the equation of the tangent plane to  at .

Explanation:

First, we need to find the partial derivatives in respect to , and , and plug in .

Remember that the general equation for a tangent plane is as follows:

Now lets apply this to our problem

### Example Question #3 : Multivariable Calculus

Let , and .

Find .

Explanation:

We are trying to find the cross product between  and .

Recall the formula for cross product.

If  , and , then

.

Now apply this to our situation.

### Example Question #4 : Multivariable Calculus

Let , and .

Find .

Explanation:

We are trying to find the cross product between  and .

Recall the formula for cross product.

If  , and , then

.

Now apply this to our situation.

### Example Question #5 : Multivariable Calculus

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

Explanation:

Remember the general equation of a line in vector form:

, where  is the starting point, and  is the difference between the start and ending points.

Lets apply this to our problem.

Distribute the

Now we simply do vector addition to get

### Example Question #6 : Multivariable Calculus

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