Question

A vector has initial point at (3,-5) and terminal point at (-2, 3). What are the characteristics of this vector?

The magnitude is 13, and the direction angle is about 58º.
The magnitude is 13, and the direction angle is about 122.
The magnitude is 789, and the direction angle is about 58º.
The magnitude is 89, and the direction angle is about 122°.

Answer 1

D. The magnitude is square-root of 89 units, and the direction angle is about 122°.

Explanation:

Answer 2

Slope of line joining the points (3,-5) and (-2, 3) is :

`m = (3-(-5))/(-2-3)\\\\m= -(8)/(5)`

Also,

`tan \theta= -(8)/(5)\\\\\theta=tan^(-1)(-(8)/(5))\\\\\theta=122^o`

Now, distance between (3,-5) and (-2, 3) is :

`d=√((3-(-2))^2+(-5-3)^2)\\\\d=√(89)\ units`

Therefore, the magnitude is
`√(89)` units, and the direction angle is about 122°.

Hence, this is the required solution.