If two collinear vectors A and B are added, the resultant has a magnitude equal to 4.0. If B is subtracted from A, the resultant has a magnitude equal to 8.0. What is the magnitude of A?

6.0

Explanation:

Given two collinear vectors A and B, if the vectors are added, the resultant will have a magnitude of 4.0. This can be expressed as;

A+B = 4 ... (1)

Similarly, if the vector difference has a resultant magnitude of 8.0, this can be expressed as;

A-B = 8 ... (2)

Solving equation 1 and 2 simultaneously;

A+B = 4 ... (1)

A-B = 8 ... (2)

Adding equation 2 to 1, the resulting equation will give;

A+A = 4+8 (note that B will cancel out)

2A = 12

A = 6.0

Therefore the magnitude of A is 6.0