If the scalar product of two vectors, and , is equal to −3.5, if , and the angle between the two vectors when they are drawn starting from the same point is equal to 130°, what is the magnitude of ?

If the scalar product of two vectors, A and C, is equal to −3.5, if |A| is 2.0, and the angle between the two vectors when they are drawn starting from the same point is equal to 130°, what is the magnitude of C?

2.7

The scalar product (also called dot product) of two vectors A and C, is given by;

A · C = |A| |C| cos β          (i)

Where;

|A| = magnitude of vector A

|C| = magnitude of vector C

β = angle between the two vectors

From the question;

|A| = 2.0

A · C = -3.5

β = 130°

Now, substitute these values into equation (i) as follows;

-3.5 = 2.0 x |C| cos 130°

-3.5 = 2.0 x |C| (-0.6428)

-3.5 = -1.2856 x |C|

|C| = 2.7

Therefore, the magnitude of vector C is 2.7