Question

the magnitude of the resultant of two vectors of magnitude 3 units and 4 units in 5 units what is the angle between two vectors​

Answer 1

A variety of mathematical operations can be performed with and upon vectors. One such operation is the addition of vectors.

Two vectors can be added together to determine the result (or resultant).

given

A = 3 units and B = 4 units let theta be angle between them. and R the resultant vector.

magnitude of R^2= { A^2 +B^2 + 2. A.B. Cos( angle between A and B) }

1= 9 + 16 + 2x 3 x 4 . cos (theta)

so

Cos(theta) = -1 , therefore theta = pi

alternatively -

R = A + B = 1 unit in magnitude

therefore the cosine term must yield a -ve value or the A and B vectors must be opposite to each other and the angle between them must be pi.

the cross product will vanish as the

A X B = A.B. Sin (angle between them) n^ = A.B. sin(pi) =0