Let a be a vector of magnitude 4.5 unit pointing due north. Evaluate the vector 3 a .

Step-by-step solution

Given that the magnitude of vector a is | a | = 4.5 units and its direction is due north. When a vector is multiplied by a positive scalar, its magnitude is multiplied by the scalar and its direction remains unchanged. The magnitude of the new vector 3 a is 3 | a | = 3 4.5 = 13.5 units. Since 3 is a positive number, the direction of 3 a is the same as a , which is due north. Thus, 3 a is 13.5 units due north.