Question

the resultant of two vectors of magnitude 3units and 4 units is 1 unit .what is magnitude of their cross product ​

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

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