Question

Consider the vectors u = <-4, 7> and v = <11, -6>. u + v = < , > ||u + v|| ≈ units

Answer 1

Answer:

5$\sqrt{2}$

Step-by-step explanation:

u + v = < - 4, 7 > + < 11, - 6 > = < - 4 + 11, 7 - 6 > = < 7, 1 >

| u + v | = $\sqrt{7^2+1^2}$ = $\sqrt{50}$ = 5$\sqrt{2}$

Answer 2

Answer:

If U = <-4, 7> , V = <11, -6> are vectors in R²:

* U + V = <7, 1>

* |U + V| = $\sqrt{50}$

Step-by-step explanation:

1. Let's define first, the sum operation between vectors U and V in R²:

* $U = V =$

⇒ $U + V =$

Where:

$u_{x} , v_{x}$ are U and V x coordinates and $u_{y} , v_{y}$ are U and V y coordinates.

In this example:

$U = V = => U + V =$

2. Let’s define secondly, length operator of a vector U in R²:

* $U =$

⇒ |U|= $\sqrt{u_{x}^2 + u_{y}^2}$

In this example:

U + V is also a vector in   R²

⇒ |U + V|= $\sqrt{(u_{x} +v_{x}) ^2 + (u_{y} +v_{y}) ^2}$

⇒ |U + V|= $\sqrt{7 ^2 + 1 ^2} = \sqrt{50}$