We have to find the absolute value of the vector z = u + v if u = i - j and v = 2i + 4j.

z = u + v

=> z = i - j + 2i + 4j

add the terms with i and those with j

=> z = 3i + 3j

The absolute value of z = 3i + 3j is

sqrt ( 3^2 + 3^2)

=> sqrt (2*9)

=> 3 sqrt 2

**Therefore the required absolute value of the vector z is 3*sqrt 2.**

To find the absolute value of z = u+v.

u = i-j.

v = 2i+4j.

Therefore u+v = (i-j)+(2i+4j) =

z = i-j+2i+4j

z = (i+2i)+(-j+4j)

z = 3i+3j.

|z| = (3^(2)+3^2)^(1/2)

|z| = 3 sqrt2 is the absolute value of z.

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**