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4.12 D) Proving that Vectors are Parallel
4.12 D) Proving that Vectors are Parallel
We are able to prove that vectors are parallel by showing that the two vectors have a common vector factor. Let’s have a few examples.
Example 1
Prove that the vectors below are parallel to one another.
Prove that the vectors below are parallel to one another.
To prove whether these two vectors are parallel to each other, we need to find a common vector factor. Both of the vectors have a common vector factor of the column vector below:
We can prove that this is the case by factorising the common vector factor out of both of the vectors.
Example 2
Prove that the vectors below are parallel.
Prove that the vectors below are parallel.
Like before, we are looking for a common vector factor for the two vectors and the common vector factor is shown below:
The next step is to factorise this common vector factor out of both of the vectors.
The final step would be to say something like: “the two vectors are parallel to one another because they have a common vector factor”.