Question:
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?
Answer:
2.7
Step-by-step explanation:
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