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Example Questions
Example Question #1 : Tangents & Normals
Find the equation of the tangent plane to at
.
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 : Tangents & Normals
Find the equation of the tangent plane to at
.
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 #1 : Dot & Cross Products
Let , and
.
Find .
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 #2 : Dot & Cross Products
Let , and
.
Find .
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 #1 : Vector Equations
Write down the equation of the line in vector form that passes through the points , and
.
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 #2 : Vector Equations
Write down the equation of the line in vector form that passes through the points , and
.
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
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