Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

The resultant of two vectors P and Q acting at a point is R. Show that if P is doubled, Q remains unaltered, then the resultant will be of the magnitude

R = √P²+Q²+2PQcosΘ ( Θ is the angle between the vectors) ⇒ R² = P²+Q²+2PQcosΘ if P is doubled & Q remains unaltered then resultant R'=√4P²+Q²+4PQcosΘ =√(2P²+2P²)+(2Q²-Q²)+4PQcosΘ =√2P²-Q²+2(P²+Q²+2PQcosΘ) =√2P²-Q²+2R² (proved)

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.

Let the angle between vectors P and Q be = Ф.

magnitude of the resultant = R, Hence, R² = P² + Q² + 2 P Q Cos Ф

Let P' = 2 P and Q as well as the angle between them Ф remains the same. Let the resultant vector be R'.

R' ² = (2 P)² + Q² + 2 (2 P) Q Cos Ф = 4 P² + Q² + 4 P Q Cos Ф = 2 (P² + Q² + 2 P Q Cos Ф) + 2 P² - Q² = 2 R² + 2 P² - Q²

Hence, the resultant now is R' = √ [ 2 R² + 2 P² - Q² ]