`vecR` is the resultant of two vectors `vecP and vecQ`. When `vecQ` is reversed , the resultant is `vecS` . Prove that `R^2+S^2=2(P^2+Q^2)`.

vecR is the resultant of the vectors vecA and vecB . If R =B/(sqrt(2)) then the angle theta is

Show that the absolute value of the resultant of two vectors vecP and vecQ cannot be greater than P+Q or less than P-Q.

The maximum magnitude of the resultant of two vectors, vec(P) and vec(Q) ("where" Pgt Q) is x times the minimum magnitude ot the resultant. When the angle between vec(P) and vec(Q)" ""is" " "theta , the magnitude of the resultant is equal to half the sum of the magnitudes of the two vectors. Prove that, cos theta =(x^2+2)/(2(1-x^2))*

Resultant of two forces P and Q is sqrt(3) Q . The resultant is inclined at 30^@ with P . Show that, either P =Q or P=2Q.

Resultant of two vectors vec(3p) and vec(2p) is R. If first vector is doubled then the resultant is also doubled. Calculate the angle between the two vectors.

Compute the resultant of three coplanar vectors P, 2P and 3P inclined at 120^@ with one another.

Resultant of vectors 3P and 2P is vector R. When the first vector is doubled, R also doubles. Find the angle between the two vectors.