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.

2 people

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.