Construct vectors A and B for the cases below. First draw a vector W, then the parallelogram that has equal and opposite vector A B as the diagonal. Then fi nd approximate magnitudes of A and B.?

Diagram needed to solve the question was missing, So I have attached it with this answer. Also the diagonals of a parallelogram can only be equal to A + B (Not AB as given in your statement).

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First of all let us understand the law of parallelogram for vector addition. It states that, "If two vectors are along the adjacent sides of a parallelogram, then their resultant is given by the vector that is a diagonal passing through the point of contact of these vectors".

I have attached the diagrams describing the vectors A and B for the cases.

From diagram, it is clear that the magnitude of A and B is equal (balancing horizontal forces) and the resultant A + B is equal to the weight of the stone W (balancing vertical forces). Therefore, we can mathematically write:

A = B - - - - - (i)

& A + B = W - - - - - - (ii)

Putting A = B in equation (ii), we get

B + B = W

2B = W

B = W/2

Putting B = W/2 in equation (i), we get

A = W/2

Hence, magnitudes of both A and B are approximately W/2