Let u = (-2,3) and v = (5,-6). Find the sum and the dot product of these two vectors.
u+v = (3,-3)
u dot v
= (-2)(5) + 3(-6)
= -10 -18 = -28
To find the sum of two vectors, you simply add their corresponding components.
Given u = (-2, 3) and v = (5, -6), the sum of these two vectors can be found as follows:
Sum = u + v
= (-2, 3) + (5, -6)
To perform the addition, add the corresponding components:
Sum = (-2 + 5, 3 + (-6))
= (3, -3)
Therefore, the sum of vectors u and v is (3, -3).
To find the dot product of two vectors, you multiply their corresponding components and sum the results.
Given u = (-2, 3) and v = (5, -6), the dot product of these two vectors is calculated as follows:
Dot Product = u · v
= (-2)(5) + (3)(-6)
= -10 + (-18)
= -28
Therefore, the dot product of vectors u and v is -28.