calculate the absolute value of the vector z=u+v if u=i-j and v=2i+4j.

The modulus of a vector has the
formula:

|z| = sqrt (x^2 + y^2), where x and y are the
coefficients of the unit vectors i and j.

First, we'll
determine the vector z:

z = u +
v

z = i - j + 2i + 4j

z = 3i +
3j

We'll identify the coefficients x and y: x = y =
3

We'll calculate the absolute value of
z:

|z| = sqrt (3^2 + 3^2)

|z|
= sqrt (9 + 9)

|z| = 3 sqrt
2