# Thread: Final tomorrow! help with vectors

1. ## Final tomorrow! help with vectors

For the two vectors given below, find .

u = 20 i + -10 j
v = 4 i + 4 j

The answer is 84.852 can somebody explain the steps?

For the two vectors given below, find .

u = 20 i + -10 j
v = 4 i + 4 j

The answer is 84.852 can somebody explain the steps?

You will need to use the following:
If $u=(u_1, u_2)$ , $v=(v_1, v_2)$ and $c$ a scalar,
$u + v=(u_1+v_1, u_2+v_2)$
$c * u=(c*u_1, c*u_2)$
$\parallel x \parallel = \sqrt {x^2}$

3. On Rn, the intuitive notion of length of the vector x = [x1, x2, ..., xn] is captured by the formula

Given: . $\begin{array}{ccc}\vec u &=& 20\vec i - 10\vec j \\ \vec v &=& 4\vec i + 4\vec j \end{array}$

Find: . $|\,\text{-}4\vec u + 5\vec v\,|$

$\text{-}4\vec u + 5\vec v \;=\;\text{-}4(20\vec i - 10\vec j) + 5(4\vec i + 4\vec j)$

. . . . . . $= \;\text{-}80\vec i + 40\vec j + 20\vec i + 20\vec j$

. . . . . . $= \;\text{-}60\vec i + 60\vec j$

$|\text{-}4\vec u + 5\vec v| \;=\;\sqrt{(\text{-}60)^2 + (60)^2} \;=\;\sqrt{7200} \;=\;60\sqrt{2} \;\approx\;84.852$