Question

A. Find a vector with the initial point (3, -2) and terminal point (7, 5).

a. <4, 7>
b. <10, 3>
c. <-4, -7>
d. <-10, -3>

b. Then, find a unit vector in the direction of <4, 7>.
a. <4/√65, 7/√65>
b. <2/√13, 7/√13>
c. <4/√65, -7/√65>
d. <-2/√13, 7/√13>

Answer 1

The vector with the initial point (3, -2) and terminal point (7, 5) is <4, 7>. The unit vector in the direction of <4, 7> is <4/sqrt(65), 7/sqrt(65)>.

Step-by-step explanation:

To find a vector with the initial point (3, -2) and terminal point (7, 5), we subtract the coordinates of the initial point from the coordinates of the terminal point. Thus, the vector is <4, 7>.

To find a unit vector in the direction of <4, 7>, we divide each component of the vector by its magnitude. The magnitude of <4, 7> is sqrt(4^2 + 7^2) = sqrt(65). So, the unit vector is <4/sqrt(65), 7/sqrt(65)>.