Answer:
5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
u + v = < - 4, 7 > + < 11, - 6 > = < - 4 + 11, 7 - 6 > = < 7, 1 >
| u + v | = [tex]\sqrt{7^2+1^2}[/tex] = [tex]\sqrt{50}[/tex] = 5[tex]\sqrt{2}[/tex]
Answer:
If U = <-4, 7> , V = <11, -6> are vectors in R²:
* U + V = <7, 1>
* |U + V| = [tex]\sqrt{50}[/tex]
Step-by-step explanation:
1. Let's define first, the sum operation between vectors U and V in R²:
* [tex]$U = <u_{x},u_{y}> V = <v_{x},v_{y}>$[/tex]
⇒ [tex]$U + V = <u_{x} + v_{x}, u_{y} + v_{y} >$[/tex]
Where:
[tex]$u_{x} , v_{x}$[/tex] are U and V x coordinates and [tex]$u_{y} , v_{y}$[/tex] are U and V y coordinates.
In this example:
[tex]$U = <-4,7> V = <11,-6}> => U + V = <7, 1>$[/tex]
2. Let’s define secondly, length operator of a vector U in R²:
* [tex]$U = <u_{x},u_{y}>$[/tex]
⇒ |U|= [tex]$ \sqrt{u_{x}^2 + u_{y}^2}$[/tex]
In this example:
U + V is also a vector in R²
⇒ |U + V|= [tex]$ \sqrt{(u_{x} +v_{x}) ^2 + (u_{y} +v_{y}) ^2}$[/tex]
⇒ |U + V|= [tex]$ \sqrt{7 ^2 + 1 ^2} = \sqrt{50} $[/tex]
