Question

If u=(4,2) and v=(-3,2) , evaluate |u+v|


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Answer 1

Answer: sqrt(17)

Step-by-step explanation

Add the components of the vectors

u+v = (4,2) + (-3,2)

u+v = (4+(-3), 2+2)

u+v = (1,4)

Then to evaluate the length of vector u = (a,b), we use this formula

|u| = sqrt(a^2+b^2)

Which is derived from the pythagorean theorem. We're looking for the hypotenuse of the right triangle formed. In this case a = 1 and b = 4.

So,

|u+v| = sqrt(1^2 + 4^2)

|u+v| = sqrt(17)