# The resultant vector P and Q is R.on reversing the direction of the angle the resultant becomes S.show that R sq.+S sq.=2(P sq.+Q sq.)

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by varshamonala

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by varshamonala

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Please draw a parallelogram AB CD. Let CD be parallel to AB. Let BC be parallel to AD. Let vector P be represented by AB. Let Q be represented by AD. Now the resultant force of P & Q is given by parallelo gram law as

R = square root [ P²+ Q² + 2 P Q cos A ] = This is diagonal AC

If the angle is reversed, That is, reverse vector AD or Q. Now draw parallelogram AEFB so that AE = - Q = - AD. FB = EA. Now the diagonal AF will be parallel to diagonal BD. The angle at A in AEFB is 180 - A. SO its cosine is - Cos A.

S = squareroot [ P² + Q² - 2 P Q cos A ]

So R² + Q² = 2 [P² + Q² ] as the other terms cancel.

This is also a relation between sides of a parallelogram and diagonals.

R = square root [ P²+ Q² + 2 P Q cos A ] = This is diagonal AC

If the angle is reversed, That is, reverse vector AD or Q. Now draw parallelogram AEFB so that AE = - Q = - AD. FB = EA. Now the diagonal AF will be parallel to diagonal BD. The angle at A in AEFB is 180 - A. SO its cosine is - Cos A.

S = squareroot [ P² + Q² - 2 P Q cos A ]

So R² + Q² = 2 [P² + Q² ] as the other terms cancel.

This is also a relation between sides of a parallelogram and diagonals.

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

So given P + Q = R

after reversing direction of R we get

- R = - P - Q

S = - P - Q

so let angle between P and Q be θ

so resultants

R² = P² +Q² +2PQCOSθ .................... i

S² = P² + Q² - 2PQCOSθ ..................... ii

SO ADDING i AND ii

R² + S² = 2(P² +Q² )

2PQCOSθ CANCELLES OUT THUS GIVING RESULT

R² + S² = 2(P² +Q² )

after reversing direction of R we get

- R = - P - Q

S = - P - Q

so let angle between P and Q be θ

so resultants

R² = P² +Q² +2PQCOSθ .................... i

S² = P² + Q² - 2PQCOSθ ..................... ii

SO ADDING i AND ii

R² + S² = 2(P² +Q² )

2PQCOSθ CANCELLES OUT THUS GIVING RESULT

R² + S² = 2(P² +Q² )