Find the inner product of a and b if a= (3, 0, –1) and b= (4, –2, 5), and state whether the vectors are perpendicular.
To find the inner product (also known as the dot product) of vectors a and b, you need to find the sum of the products of their corresponding components.
1. Multiply the corresponding components of vectors a and b:
a • b = (3 * 4) + (0 * -2) + (-1 * 5) = 12 + 0 - 5 = 7
2. The result of the inner product is 7.
To determine if the vectors are perpendicular, you can check if the inner product is zero. If it is, then the vectors are perpendicular.
In this case, since the inner product is not zero (7 ≠ 0), the vectors a and b are not perpendicular.