Is vector v with an initial point of (-5,22) and a terminal point of (20,60) equal to vector u with an intintal point of (50,120) and a terminal point of (75,158)

Question

asked Jul 21, 2020 205k views

2 Answers

Nathan Bellowe · Answer 1 · 2020-07-26T23:42:17+0000

Answer:

Yes, vectors u and v are equal.

Explanation:

We need to check whether vectors u and v are equal or not.

If the initial point is
(x_1,y_1) and terminal point is
(x_2,y_2) , then the vector is

Vector=(x_2-x_1)i+(y_2-y_1)j

Vector v with an initial point of (-5,22) and a terminal point of (20,60).

$\overrightarrow v=(20-(-5))i+(60-22)j$

$\overrightarrow v=25i+38j$ ..... (1)

Vector u with an initial point of (50,120) and a terminal point of (75,158).

$\overrightarrow u=(75-50)i+(158-120)j$

$\overrightarrow u=25i+38j$ .... (2)

From (1) and (2) we get

$\overrightarrow u=\overrightarrow v$

Therefore, vectors u and v are equal.