Vector A has a magnitude of 25 units and points in the positive y-direction. When vector B is added to A, the resultant vector A B points in the negative y-direction with a magnitude of 15 units. Find the magnitude and direction of B.

B= -40

The negative sign indicates the reverse direction to that of vector A.That is it is in the third quadrant.

Explanation:

Th resultant vector is obtained by adding the two vectors A and B

A + B= AB

25 + B= -15

25+ 15= -B

-B = 40

B= -40

Vector B has a magnitude of 40 and points in the opposite direction to that of vector A. The negative indicates the opposite direction.

When we reverse the vector B for adding we place a negative sign with the magnitude.

A vector is quantity defined by magnitude and direction. If the direction is left out it becomes a scalar.

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