If is vector a ia 7 units long, the magnitude of vector b is 10 units and the cosine of the angle between the two vectors is -0.3 when they are placed tail-to-tail, what does the inner product of vector a and vector b equal?
To find the inner product of two vectors, we can use the formula:
A · B = |A| * |B| * cos(θ)
where A · B represents the inner product of vectors A and B, |A| and |B| represent the magnitudes of vectors A and B, and θ represents the angle between the two vectors.
In this case, we are given that the magnitude of vector A is 7 units (|A| = 7), the magnitude of vector B is 10 units (|B| = 10), and the cosine of the angle between the two vectors when placed tail-to-tail is -0.3 (cos(θ) = -0.3).
Plugging these values into the formula, we have:
A · B = 7 * 10 * (-0.3)
= -21
Therefore, the inner product of vector A and vector B is -21 units.