Final answer:
To find the dot product of the vectors a = 5i + 5j − k and b = −4i + 9k, multiply corresponding components and sum the results, which gives us a dot product of −29.
Step-by-step explanation:
The question asks us to find the dot product of two vectors a and b. The vectors are given by a = 5i + 5j − k, and b = −4i + 9k. The dot product, also known as the scalar product, of two vectors can be calculated by multiplying their corresponding components and summing these products.
- Multiply the i components: (5)(−4) = −20
- Multiply the j components: (5)(0) = 0
- Multiply the k components: (−1)(9) = −9
Summing these gives us the dot product: −20 + 0 + −9 = −29.
Therefore, the dot product of vectors a and b is −29.