
What does a dot product equal to one mean?
Answer
417k+ views
Hint: We need to have a basic idea of what a dot product actually means. There are many definitions of dot products. We use the basic definition which states dot product or scalar product is given by: where is the angle between two given vectors.
Complete step by step solution:
The dot product is also called a scalar product. This states that multiplying any two vectors will give us a single vector which is scalar. Here we have considered the vectors as A and B
Scalar product or dot product is basically defined as a product of 2 vectors along with the angle of cosine between them. Look at the formula above , we have written 2 terms , these are called magnitudes of vectors(it is the length of the vector).
According to the question they have given that the dot product is 1. It means that
Or,
This is possible only when : ,
And , means that the angle between the 2 vectors A and B is zero.
Hence the 2 vectors are parallel. To get better idea look at the image shown below:
Now the fact that the angle between 2 vectors is 0 means that the vector could be parallel or antiparallel as shown in the image below;
Hence if the dot product is 1 it means that the two given vectors are parallel. And if the dot product is -1 it means that the two given vectors are antiparallel.
Additional Information:
If the angle between 2 given vectors is it means that and they are said to be orthogonal.
he dot product of a unit vector with itself is given by:
Note:
We should remember that the angle being 0 doesn’t mean that the vectors are only parallel; they can also be antiparallel. Thus when the dot product is 1 it means the vectors are parallel and when the dot product is-1 it means the vectors are anti-parallel.
Complete step by step solution:
The dot product is also called a scalar product. This states that multiplying any two vectors will give us a single vector which is scalar. Here we have considered the vectors as A and B
Scalar product or dot product is basically defined as a product of 2 vectors along with the angle of cosine between them. Look at the formula above , we have written 2 terms
According to the question they have given that the dot product is 1. It means that
Or,
This is possible only when :
And
Hence the 2 vectors are parallel. To get better idea look at the image shown below:

Now the fact that the angle between 2 vectors is 0 means that the vector could be parallel or antiparallel as shown in the image below;

Hence if the dot product is 1 it means that the two given vectors are parallel. And if the dot product is -1 it means that the two given vectors are antiparallel.
Additional Information:
Note:
We should remember that the angle being 0 doesn’t mean that the vectors are only parallel; they can also be antiparallel. Thus when the dot product is 1 it means the vectors are parallel and when the dot product is-1 it means the vectors are anti-parallel.
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