Find the specified vector or scalar. Show your work.

u = -4i + 1j and v = 4i + 1j; Find ‖𝑢 + 𝑣‖.

I am not sure I understand your symbol. (absolute value?)

anyway
u + v = 2 j

the magnitude of 2 j is 2

Can you show your work please ? and that's what the question says exactly

to add two vectors you can add the components in orthogonal (perpendicular) directions and the sum will have components in those directions

if u = a i + b j
and v = c i + d j
then
u + v = (a+c) i + (b+d) j
now here
u+v = (-4+4) i + (1+1) j
or
0 i + 2 j
which is magnitude 2 in the j (or y) direction because j is a unit vector in the y direction.

Thank you !! Can you help with my other two questions i had post ?

To find the magnitude of the vector sum (u + v), we need to perform the following steps:

Step 1: Add the corresponding components of u and v to obtain the vector sum (u + v).
(u + v) = (-4i + 1j) + (4i + 1j)
= (-4i + 4i) + (1j + 1j)
= 0i + 2j
= 2j

Step 2: Find the magnitude of the vector (u + v).

The magnitude of a vector can be calculated using the formula:
‖𝑢‖ = √(𝑎^2 + 𝑏^2)

In this case, since our vector (u + v) = 2j, we can substitute its components into the formula:
‖𝑢 + 𝑣‖ = √(0^2 + 2^2)
= √(0 + 4)
= √4
= 2

Therefore, the magnitude of the vector ‖𝑢 + 𝑣‖ is 2.