Suppose vector a is 3 units long, the magnitude of vector b is 1 units and cos (θ) = -0.3, where θ is the angle between the two vectors when they are placed tail-to-tail. What does the inner product of vector a and vector b equal?
a.b = |a|*|b|*cosθ
= 3 * 1 * (-.3) = -.9
To find the inner product (also known as the dot product) of two vectors, you need to multiply their magnitudes and the cosine of the angle between them.
Given:
Magnitude of vector a, |a| = 3 units
Magnitude of vector b, |b| = 1 unit
Cosine of the angle between them, cos(θ) = -0.3
To find the inner product, follow these steps:
Step 1: Multiply the magnitudes of the two vectors.
|a| * |b| = 3 * 1 = 3
Step 2: Multiply the result from Step 1 by the cosine of the angle between the vectors.
Inner product = 3 * cos(θ)
Since we know that cos(θ) = -0.3, we can substitute that value in the equation.
Inner product = 3 * (-0.3)
Inner product = -0.9
Therefore, the inner product of vector a and vector b is -0.9.