State parallelogram law of vectors . Der...

State parallelogram law of vectors . Derive an expression for the magnitude and direction of the resultant vector .

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Paralleogram Law : If two vectors are represented by the two adjacent sides of a parallelogram then the diagonal passing through the intersection of given vectors represents their resultant both in direction and magnitude .

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If the angle between two vectors of equal magnitude P is theta , the magnitude of the resultant vector is

`2P "cos" (theta)/(2)`

`2P "sin " (theta)/(2)`

`2P cos theta`

`2P sin theta`

The resultant of two vectors vecP and vecQ is vecR If the magnitude of vecQ is doubled, the new resultant becomes perpendicular to vecP , the the magnitude of vecR is

`(P^(2)-Q)/(2PQ)`

`(P+Q)/(P-Q)`

`(P)/(Q)`

The resultant of two vectors vecP and vecQ is vecR . If the magnitude of vecQ is doubled, the new resultant becomes perpendicular to vecP , then the magnitude of vecR is

`(P^(2)-Q)/(2PQ)`

`2(P+Q)/(P-Q)`

`P/Q`