All High School Math Resources
Example Questions
Example Question #1 :Calculus Ii — Integrals
Find the vector where its initial point isand its terminal point is.
We need to subtract the-coordinate and the-coordinates to solve for a vector when given its initial and terminal coordinates:
Initial pt:
Terminal pt:
Vector:
Vector:
Example Question #1 :Parametric, Polar, And Vector
Find the vector where its initial point isand its terminal point is.
We need to subtract the-coordinate and the-coordinate to solve for a vector when given its initial and terminal coordinates:
Initial pt:
Terminal pt:
Vector:
Vector:
Example Question #11 :Calculus Ii — Integrals
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 #1 :Understanding Vector Calculations
Find the magnitude of vector:
To solve for the magnitude of a vector, we use the following formula:
Example Question #1 :Understanding Vector Calculations
Given vectorand, solve for.
To solve for, we need to add thecomponents in the vector and thecomponents together:
Example Question #1 :Parametric, Polar, And Vector
Given vectorand, solve for.
To solve for, we need to subtract thecomponents in the vector and thecomponents together:
Example Question #1 :Understanding Vector Calculations
Given vectorand, solve for.
To solve for, We need to first multiplyinto vectorto findand multiplyinto vectorto find; then we need to subtract thecomponents in the vector and thecomponents together:
Example Question #16 :Calculus Ii — Integrals
Find the unit vector of.
To solve for the unit vector, the following formula must be used:
unit vector:
Example Question #2 :Understanding Vector Calculations
Isa unit vector?
yes, because magnitude is equal to
no, because magnitude is not equal to
not enough information given
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 #18 :Calculus Ii — Integrals
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