Respuesta :
Answer: u.(v+w) = -20
Step-by-step explanation:
Given;
u = -i+j
v = 10i-2j
w = -8j
v+w = 10i-2j +(-8j)
v+w = 10i-10j
u .(v+w) = (-i+j).(10i-10j)
= -1×10 + 1 ×-10
= -10-10
u.(v+w) = -20
Answer: u(v+w) = - 20
Step-by-step explanation: u, v and w are vectors in the x-y plane, where i is related to the x-axis and j is related to the y-axis. Vectors can be added, subtracted or "perform" an operation called dot product.
In this question, we have: u.(v + w)
To resolve it, first add the vectors:
(v + w) = (10i - 2j) + (-8j)
(v + w) = (10i - 10j)
Now, the dot product:
u . (v + w) = (-i + j) . (10i - 10j)
u . (v + w) = (-1)(10) + (1).(-10)
u . (v + w) = - 10 - 10
u . (v + w) = - 20
Note that the sum of vector gave another vector. However, the dot product of vectors produce a scalar because it's the sum of the product of the horizontal elements with the sum of the product of the vertical elements.
