All Calculus 3 Resources
Example Questions
Example Question #1 :Cross Product
Let, and.
Find.
We are trying to find the cross product betweenand.
Recall the formula for cross product.
If, and, then
.
Now apply this to our situation.
Example Question #2 :Cross Product
Let, and.
Find.
We are trying to find the cross product betweenand.
Recall the formula for cross product.
If, and, then
.
Now apply this to our situation.
Example Question #3 :Cross Product
True or False: The cross product can only be taken of two 3-dimensional vectors.
False
True
True
This is true. The cross product is defined this way. The dot product however can be taken for two vectors of dimension n (provided that both vectors are the same dimension).
Example Question #4 :Cross Product
Which of the following choices is true?
By definition, the order of the dot product of two vectors does not matter, as the final output is a scalar. However, the cross product of two vectors will change signs depending on the order that they are crossed. Therefore
.
Example Question #5 :Cross Product
For what angle(s) is the cross product?
We have the following equation that relates the cross product of two vectorsto the relative angle between them, written as
.
From this, we can see that the numerator, or cross product, will bewhenever. This will be true for all even multiples of. Therefore, we find that the cross product of two vectors will befor.
Example Question #6 :Cross Product
Evaluate
None of the other answers
None of the other answers
It is not possible to take the cross product of-component vectors. The definition of the cross product states that the two vectors must each havecomponents. So the above problem is impossible.
Example Question #7 :Cross Product
Compute.
To evaluate the cross product, we use the determinant formula
So we have
. (Use cofactor expansion along the top row. This is typically done when taking any cross products)
Example Question #8 :Cross Product
Evaluate.
None of the other answers
To evaluate the cross product, we use the determinant formula
So we have
. (Use cofactor expansion along the top row. This is typically done when taking any cross products)
Example Question #9 :Cross Product
Find the cross product of the two vectors.
To find the cross product, we solve for the determinant of the matrix
The determinant equals
As the cross-product.
Example Question #10 :Cross Product
Find the cross product of the two vectors.
To find the cross product, we solve for the determinant of the matrix
The determinant equals
As the cross-product.
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