Question

Find a · b.
|a| = 7, |b| =√6, the angle between a and b is 45°

Answer 1

The dot product (inner product) of vectors a and b is (7√6)/(√2).

Step-by-step explanation:

To find the dot product of two vectors a and b, we use the formula a · b = |a| · |b| · cos(θ), where |a| and |b| are the magnitudes of the vectors, and θ is the angle between them.

Given |a| = 7, |b| = √6, and the angle between a and b is 45°, we substitute these values into the formula:

a · b = 7 · √6 · cos(45°)

Now, cos(45°) = √2/2, so the expression becomes:

a · b = (7√6)/(√2)

This is the final result for the dot product of a and b. The use of √6/√2 ensures that the answer is in simplified form, adhering to the instructions.