Calculus 3 : Vectors and Vector Operations
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Example Questions
Example Question #331 : Vectors And Vector Operations
Given the following two vectors, 
The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.
Note that the dot product is a scalar value rather than a vector; there's no directional term.
Now considering our problem, we're given the vectors 
The dot product can be found following the example above:
Example Question #2334 : Calculus 3
Given the following two vectors, 
The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.
Note that the dot product is a scalar value rather than a vector; there's no directional term.
Now considering our problem, we're given the vectors 
The dot product can be found following the example above:
Example Question #18 : Dot Product
Given the following two vectors, 
The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.
Note that the dot product is a scalar value rather than a vector; there's no directional term.
Now considering our problem, we're given the vectors 
The dot product can be found following the example above:
Example Question #19 : Dot Product
Given the following two vectors, 
The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.
Note that the dot product is a scalar value rather than a vector; there's no directional term.
Now considering our problem, we're given the vectors 
The dot product can be found following the example above:
Example Question #13 : Dot Product
Given the following two vectors, 
The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.
Note that the dot product is a scalar value rather than a vector; there's no directional term.
Now considering our problem, we're given the vectors 
The dot product can be found following the example above:
Example Question #332 : Vectors And Vector Operations
Given the following two vectors, 
The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.
Note that the dot product is a scalar value rather than a vector; there's no directional term.
Now considering our problem, we're given the vectors 
The dot product can be found following the example above:
Example Question #333 : Vectors And Vector Operations
Given the following two vectors, 
The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.
Note that the dot product is a scalar value rather than a vector; there's no directional term.
Now considering our problem, we're given the vectors 
The dot product can be found following the example above:
Example Question #334 : Vectors And Vector Operations
Given the following two vectors, 
The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.
Note that the dot product is a scalar value rather than a vector; there's no directional term.
Now considering our problem, we're given the vectors 
The dot product can be found following the example above:
Note that since the dot product is zero, these two vectors are perpendicular!
Example Question #335 : Vectors And Vector Operations
Given the following two vectors, 
The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.
Note that the dot product is a scalar value rather than a vector; there's no directional term.
Now considering our problem, we're given the vectors 
The dot product can be found following the example above:
Example Question #25 : Dot Product
Given the following two vectors, 
The dot product of a paired set of vectors can be found by summing up the individual products of the multiplications between matched directional vectors.
Note that the dot product is a scalar value rather than a vector; there's no directional term.
Now considering our problem, we're given the vectors 
The dot product can be found following the example above:
If there is confusion about how the above result is met, note the trigonometric identity:
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