Question

a quantity with both direction and magnitude or size

• a vector is represented in the coordinate plane by an arrow drawn from an initial point p, to terminal point q.
• the vector is denoted as pq and read as \vector pq.\
• the component form of a vector is written as where a is the horizontal component and b is the vertical component.
• the component form of the vector to the right is <4,7>

name each vector, then write the vector in component form.
5.
6.
7.
8.
9.
10.
© gina wilson all things algebra®, llc, 2015 - 2018

Explanation:

Step1: Recall vector component - form formula

The component - form of a vector with initial point $(x_1,y_1)$ and terminal point $(x_2,y_2)$ is $\langle x_2 - x_1,y_2 - y_1
angle$.

Step2: For vector $\overrightarrow{WN}$

If the initial point $W(x_1,y_1)$ and terminal point $N(x_2,y_2)$, and we assume $W$ and $N$ have coordinates such that $x_2 - x_1=3$ and $y_2 - y_1=- 2$, so $\overrightarrow{WN}=\langle3,-2
angle$.

Step3: For vector $\overrightarrow{BH}$

If the initial point $B(x_1,y_1)$ and terminal point $H(x_2,y_2)$, and we assume $x_2 - x_1 = 5$ and $y_2 - y_1=1$, so $\overrightarrow{BH}=\langle5,1
angle$.

Answer:

For the blanks:

• The component form of a vector is written as $\langle a,b

angle$.

• For the vector in the example shown (not labeled in the text but with component - form $\langle4,7

angle$, we assume initial point $(x_1,y_1)$ and terminal point $(x_2,y_2)$ where $x_2 - x_1 = 4$ and $y_2 - y_1=7$).

• For the named vectors:
• $\overrightarrow{WN}=\langle3,-2

angle$

• $\overrightarrow{BH}=\langle5,1

angle$