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Example Questions
Example Question #1 : Dot Product
Evaluate the dot product between , and
.
All we need to do is multiply like components.
Example Question #2 : Dot Product
Evaluate the dot product of , and
.
All we need to do is multiply the like components and add them together.
Example Question #3 : Dot Product
Find the dot product of the following vectors:
To find the dot product between two vectors
we calculate
so for
we have
Example Question #4 : Dot Product
What is the length of the vector
?
We can compute the length of a vector by taking the square root of the dot product of and
, so the length of
is:
Example Question #5 : Dot Product
Find the dot product of the following vectors:
To find the dot product between two vectors
we calculate
so for
we have
Example Question #6 : Dot Product
What is the length of the vector
?
We can compute the length of a vector by taking the square root of the dot product of and
, so the length of
is:
Example Question #7 : Dot Product
Which of the following cannot be used as a definition of the dot product of two real-valued vectors?
, where
is the angle between
.
They may all be used
is not correct. This is saying effectively to add all the components of the two vectors together. The other two definitions are commonly used in computing angles between vectors and other objects, and can also be derived from each other.
Example Question #8 : Dot Product
Which of the following is true concerning the dot product of two vectors?
The dot product of two vectors is never negative.
The dot product of two vectors is never a scalar.
if and only if
are orthogonal.
is well-defined as long as each vector is the same dimension
None of the other statements are true.
if and only if
are orthogonal.
This statement is true; it can be derived from the definition by setting the acute angle between the vectors to be
; the requirement for orthogonality. Additionally, if either vector has length
, the vectors are still said to be orthogonal.
Example Question #9 : Dot Product
What is the dot product of vectors and
?
Let vector be represented as
and vector
be represented as
.
The dot product of the vectors and
is
.
In this problem
Example Question #10 : Dot Product
What is the dot product of vectors and
?
Does not exist
Let vector be represented as
and vector
be represented as
.
The dot product of the vectors and
is
.
In this problem
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