How do you find the dot product of vectors a and b where a = 6i + 5j and b = 5i + 4j?

The dot product of two vectors can be calculated using the formula:

• a . b = |a| |b| cos(theta)
• Or more directly for vectors in component form:
• a . b = a_x * b_x + a_y * b_y

In this case, vectors a and b are given as:

• a = 6i + 5j
• b = 5i + 4j

To find the dot product:

1. Identify the components of each vector:
• a_x = 6, a_y = 5
• b_x = 5, b_y = 4
2. Plug the components into the dot product formula:
• a . b = (6 * 5) + (5 * 4)
• a . b = 30 + 20
• a . b = 50

Therefore, the dot product of vectors a and b is 50.