Answer:
The terminal point of the given vector is (9,3).
Step-by-step explanation:
The given vector is
[tex]\mathbf{a}=\left<5,2\right>[/tex]
If initial point is [tex]P(x_1,y_1)[/tex] and terminal point is [tex]Q(x_2,y_2)[/tex], then vector PQ is defined as
[tex]\overrightarrow{PQ}=<x_2-x_1,y_2-y_1>[/tex]
Initial point is P=(4,1). Let (a,b) are the coordinates of terminal point.
[tex]<5,2>=<a-4, b-1>[/tex]
On comparing both sides we get
[tex]a-4=5\Rightarrow a=5+4\Rightarrow a=9[/tex]
[tex]b-1=2\Rightarrow b=2+1\Rightarrow b=3[/tex]
Therefore, the terminal point of the given vector is (9,3).
