A vector d has a magnitude of2.6 m and points north. What are the magnitudes and directions of the vectors (a) - d, (b) d/2.0, (c) - 2.5d, and (d) 5.0d?

Solution :

A vector is defined as an element that has magnitude of some measure and direction.

It is given there is vector 'd' which has magnitude 2.6 m and its direction is towards north.

a). -d

    The magnitude of the vector '-d' is 2.6 m and its direction is reversed, i.e. its direction is towards south.

b). d/2.0

  The magnitude of the vector 'd/2.0' is 1.3 m and its direction is towards north.

c). - 2.5d

  The magnitude of the vector increases by 2.5 times i.e. 2.5 x 2.6 = 6.5 m and the direction is towards south.

d). 5.0d

    The magnitude of the vector increases by 5 times i.e. 5 x 2.6 = 13 m and the direction is towards north.