Question

review the graph. what is the component form and magnitude of the vector shown? (-2,7) and √53 (-2,7) and 53 (-7,2) and √53 (-7,2) and 53

Explanation:

Step1: Find component - form

If the initial point of the vector is $(x_1,y_1)$ and the terminal point is $(x_2,y_2)$, the component - form of the vector $\vec{v}=\langle x_2 - x_1,y_2 - y_1
angle$. Assume the initial point is $(6,2)$ and the terminal point is $(4,9)$. Then $x_2 - x_1=4 - 6=-2$ and $y_2 - y_1=9 - 2 = 7$, so the component - form is $\langle-2,7
angle$.

Step2: Calculate magnitude

The magnitude of a vector $\vec{v}=\langle a,b
angle$ is given by $|\vec{v}|=\sqrt{a^{2}+b^{2}}$. Here $a=-2$ and $b = 7$, so $|\vec{v}|=\sqrt{(-2)^{2}+7^{2}}=\sqrt{4 + 49}=\sqrt{53}$.

Answer:

A. $(- 2,7)$ and $\sqrt{53}$