# The angle between P and Q?

#### Indranil

The resultant R of vectors P and Q is perpendicular to P and R=P both, then the angle between P and Q is what?
Now, what is the concept behind it? Could you provide me with an image of the resultant perpendicular to two vectors so that I can understand the concept and start solving the problem?

#### ChipB

PHF Helper
Please clarify what you mean by the phrase "R=P both" - are you trying to say that the magnitude of vector R = the magnitude of vector P?

Keep in mind that for vector R (which is the sum of vectors P and Q) to be perpendicular to P, the vector Q must have a component in the negative P direction that is equal in magnitude to the magnitude of P, and Q must also have a component that is perpendicular to P.

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#### Indranil

Please clarify what you mean by the phrase "R=P both" - are you trying to say that the magnitude of vector R = the magnitude of vector P?

Keep in mind that for vector R (which is the sum of vectors P and Q) to be perpendicular to P, the vector Q must have a component in the negative P direction that is equal in magnitude to the magnitude of P, and Q must also have a component that is perpendicular to P.
Could you please get your points a little bit easier with a diagram so that I can understand the concept well?

#### studiot

Go back to you original definition of vector addition by the parallelogram law.

Start by drawing vector P.

From the same origin O, draw vector R the same length and at right angles to P.
This will be the diagonal resultant of your parallelogram.

Join the ends of the vectors R and P, noting the angle alpha as shown.

Complete the parallelogram by drawing the vector OQ parallel to RP.

Thus you can find the angle required by simple geometry.

I will leave it to ChipB use these diagrams to explain what he means by components if he wants.

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• 2 people

#### Indranil

Go back to you original definition of vector addition by the parallelogram law.

Start by drawing vector P.

From the same origin O, draw vector R the same length and at right angles to P.
This will be the diagonal resultant of your parallelogram.

Join the ends of the vectors R and P, noting the angle alpha as shown.

Complete the parallelogram by drawing the vector OQ parallel to RP.

Thus you can find the angle required by simple geometry.

I will leave it to ChipB use these diagrams to explain what he means by components if he wants.
Thanks a lot. So kind of you.