Question

two vectors in cartesian coordinates have components a⃗ = (3, 4, 2) and b⃗ = (4, -1, 7). show answer no attempt what is the dot product of vector a⃗ with vector b⃗ ?

Answer 1

The dot product of vector a = (3, 4, 2) with vector b = (4, -1, 7) is calculated by the formula (3 × 4 + 4 × -1 + 2 × 7), resulting in a dot product of 22.

Step-by-step explanation:

The dot product of two vectors in Cartesian coordinates is computed by multiplying their corresponding components and then adding the products together. For vectors a = (3, 4, 2) and b = (4, -1, 7), the dot product is calculated as follows:

a ⋅ b = (3 × 4) + (4 × -1) + (2 × 7)

a ⋅ b = 12 - 4 + 14

a ⋅ b = 22

Therefore, the dot product of vector a with vector b is 22.