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Example Questions
Example Question #1 : Vectors And Vector Operations
What is the angle between the vectors and
?
To find the angle between vectors, we must use the dot product formula
where is the dot product of the vectors
and
, respectively.
and
are the magnitudes of vectors
and
, respectively.
is the angle between the two vectors.
Let vector be represented as
and vector
be represented as
.
The dot product of the vectors and
is
.
The magnitude of vector is
and vector
is
.
Rearranging the dot product formula to solve for gives us
For this problem,
The two vectors are parallel.
Example Question #3 : Vectors And Vector Operations
Find the approximate acute angle in degrees between the vectors .
None of the other answers
To find the angle between two vectors, use the formula
.
Example Question #8 : Angle Between Vectors
Find the angle between the following two vectors.
In order to find the angle between two vectors, we need to take the quotient of their dot product and their magnitudes:
Therefore, we find that
.
Example Question #1 : Angle Between Vectors
Find the (acute) angle between the vectors in degrees.
To find the angle between vectors, we use the formula
.
Substituting in our values, we get
Example Question #10 : Angle Between Vectors
Find the angle between the two vectors.
No angle exists
To find the angle between two vector we use the following formula
and solve for .
Given
we find
Plugging these values in we get
To find we calculate the
of both sides
and find that
Example Question #21 : Calculus 3
Find the angle between the two vectors.
No angle exists
To find the angle between two vector we use the following formula
and solve for .
Given
we find
Plugging these values in we get
To find we calculate the
of both sides
and find that
Example Question #21 : Calculus 3
Find the approximate angle in degrees between the vectors .
None of the other answers
We can compute the (acute) angle between the two vectors using the formula
Hence we have
Example Question #12 : Angle Between Vectors
Find the angle in degrees between the vectors .
None of the other answers
None of the other answers
The correct answer is approximately degrees.
To find the angle between two vectors, we use the equation .
Hence we have
(This answer is small due to the fact that the two vectors nearly point in the same direction, due to and
being close in value.)
Example Question #12 : Angle Between Vectors
Find the acute angle in degrees between the vectors .
None of the other answers
To find the angle between two vectors, we use the formula
.
So we have
Example Question #11 : Angle Between Vectors
Find the angle between the following vectors (to two decimal places):
0.98
1.18
1.46
1.62
2.89
1.46
The dot product is defined as:
Where theta is the angle between the two vectors. Solving for theta:
To solve each component:
Putting it all together, we can solve for theta:
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