Final answer:
The dot product of vectors a = 4i + 3j - 2k and b = -3i + 5j - k is calculated by multiplying corresponding components and summing the results, which is 5.
Step-by-step explanation:
To find the dot product of two vectors a and b, we multiply the corresponding components of each vector and then sum those products. Given vectors a = 4i + 3j - 2k and b = -3i + 5j - k, the dot product is calculated as follows:
- Multiply the corresponding components of the vectors: (4)(-3), (3)(5), and (-2)(-1).
- Add these values together to find the dot product: (4)(-3) + (3)(5) + (-2)(-1) = -12 + 15 + 2 = 5.
The dot product of vectors a and b is 5.