Inner Product Calculator

Formula

The formula to calculate the inner product of two vectors is:

\[ a \cdot b = M_a \cdot M_b \cdot \cos(x) \]

Where:

\( a \) and \( b \) are vectors
\( M_a \) and \( M_b \) are the magnitudes of those two vectors
\( x \) is the angle between vectors \( a \) and \( b \)

What is an Inner Product?

An inner product is a mathematical scalar value of the multiplication of two or more vectors of an undetermined size. It is calculated by multiplying the magnitudes of the vectors by the cosine of the angle between them.

Example Calculation

Let's assume the following values:

Magnitude of Vector \( a \) (\( M_a \)): 5
Magnitude of Vector \( b \) (\( M_b \)): 3
Angle between Vectors (\( x \)): 60 degrees

Step 1: Calculate the inner product:

\[ a \cdot b = 5 \cdot 3 \cdot \cos(60^\circ) = 5 \cdot 3 \cdot 0.5 = 7.5 \]

Therefore, the inner product of the vectors is 7.5.