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.
idk sorry
inner product or dot product
= 3(4) + 0 -1(5) = 12-5 = 7
not perpendicular, (would have to be zero)
To find the inner product (also known as dot product) of two vectors, you need to perform the following operation:
a · b = (3 * 4) + (0 * -2) + (-1 * 5)
Simplifying the expression:
a · b = 12 + 0 + (-5)
a · b = 7
Therefore, the inner product of vectors a and b is 7.
To determine whether the vectors are perpendicular, we need to check if their inner product is equal to zero. If the inner product of two vectors is zero, it means they are perpendicular to each other.
In this case, since the inner product is not equal to zero (7 ≠ 0), vectors a and b are not perpendicular to each other.