
How do we find out if vectors are parallel?
Answer
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Hint: In the given question, we have been asked to find out a way to know whether the given vectors are parallel or not. In order to check that the any two given vectors are parallel, then let say two vectors A and B are parallel if and only if they are scalar multiples of one another i.e. , k is a constant not equal to zero. The alternative way to find out the two vectors are parallel is that the angle between those vectors must be equal to .
Formula used:
Two vectors A and B are parallel if and only if they are scalar multiples of one another.
Condition under which vectors and are parallel is given by
Or
Complete step-by-step answer:
Two vectors A and B are parallel if and only if they are scalar multiples of one another.
, k is a constant not equal to zero.
Let and
A and B are parallel if and only if
Therefore,
Now,
And
Or
And
Condition under which vectors and are parallel is given by
Or
.
Alternative method:
If two vectors are parallel, then angle between those vectors must be equal to
We can find the cross product of both the vectors.
So,
Therefore, to show two vectors are parallel, then find the angle between them.
Note: Whenever such a type of question is given, where we need to find whether the given vectors are parallel or not. Find the cross products of the two vectors, if the cross product is equal to zero then the given vectors are parallel otherwise not. You can also use the condition that two vectors are parallel if and only if they are scalar multiples of one another otherwise they are not parallel.
Formula used:
Two vectors A and B are parallel if and only if they are scalar multiples of one another.
Condition under which vectors
Or
Complete step-by-step answer:
Two vectors A and B are parallel if and only if they are scalar multiples of one another.
Let
A and B are parallel if and only if
Therefore,
Now,
Or
Condition under which vectors
Or
Alternative method:
If two vectors are parallel, then angle between those vectors must be equal to
We can find the cross product of both the vectors.
So,
Therefore, to show two vectors are parallel, then find the angle between them.
Note: Whenever such a type of question is given, where we need to find whether the given vectors are parallel or not. Find the cross products of the two vectors, if the cross product is equal to zero then the given vectors are parallel otherwise not. You can also use the condition that two vectors are parallel if and only if they are scalar multiples of one another otherwise they are not parallel.
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