All High School Math Resources
Example Questions
Example Question #1 :Understanding Vector Calculations
Letbe vectors. All of the following are defined EXCEPT:
The cross product of two vectors (represented by "x") requires two vectors and results in another vector. By contrast, the dot product (represented by "") between two vectors requires two vectors and results in a scalar, not a vector.
If we were to evaluate, we would first have to evaluate, which would result in a scalar, because it is a dot product.
However, once we have a scalar value, we cannot calculate a cross product with another vector, because a cross product requires two vectors. For example, we cannot find the cross product between 4 and the vector <1, 2, 3>; the cross product is only defined for two vectors, not scalars.
The answer is.
Example Question #2 :Understanding Vector Calculations
Find the magnitude of vector:
To solve for the magnitude of a vector, we use the following formula:
Example Question #3 :Understanding Vector Calculations
Given vectorand, solve for.
To solve for, we need to add thecomponents in the vector and thecomponents together:
Example Question #11 :Calculus Ii — Integrals
Given vectorand, solve for.
To solve for, we need to subtract thecomponents in the vector and thecomponents together:
Example Question #5 :Understanding Vector Calculations
Given vectorand, solve for.
To solve for,我们首先需要相乘into vectorto findand multiplyinto vectorto find; then we need to subtract thecomponents in the vector and thecomponents together:
Example Question #6 :Understanding Vector Calculations
Find the unit vector of.
To solve for the unit vector, the following formula must be used:
unit vector:
Example Question #7 :Understanding Vector Calculations
Isa unit vector?
yes, because magnitude is equal to
not enough information given
no, because magnitude is not equal to
yes, because magnitude is equal to
To verify where a vector is a unit vector, we must solve for its magnitude. If the magnitude is equal to 1 then the vector is a unit vector:
is a unit vector because magnitude is equal to.
Example Question #8 :Understanding Vector Calculations
Given vector. Solve for the direction (angle) of the vector:
To solve for the direction of a vector, we use the following formula:
=
with the vector being
Example Question #1 :Understanding Vector Calculations
Solve for vectorgiven direction ofand magnitude of.
To solve for a vector with the magnitude and direction given, we use the following formula:
Example Question #10 :Understanding Vector Calculations
Given vectorand, solve for.
To solve for, We need to multiplyinto vectorto find; then we need to subtract thecomponents in the vector and thecomponents together: