Answer:
- the drawing is attached
- component form: -9i -12j
- magnitude∠direction = 15∠233.13°
- unit vector: -0.6i -0.8j = 1∠233.13°
Explanation:
You want a drawing of the vector between (1, 3) and (-8, -9), along with its component form as sum of unit vectors i and j, its magnitude and direction, and the corresponding unit vector.
Drawing
See the attachment for the drawing.
Component form
The difference between the head and tail coordinates is ...
(-8, -9) -(1, 3) = (-9, -12)
That is, the vector extends -9 units in the +x direction, and -12 units in the +y direction, so its component form is ...
-9i -12j
Polar form
The magnitude of a vector is the root of the sum of squares of its components:
|v| = √((-9)² +(-12)²) = √(81+144) = √225
|v| = 15
The direction can be found using the arctangent function:
∠v = arctan(-12/-9) = 180° +51.13° . . . . . accounting for quadrant
∠v = = 233.13°
Unit vector
The unit vector in the same direction is found by replacing the magnitude in polar form by 1.
u = 1∠233.13°
The component form is found by dividing the vector by its magnitude:
u = v/|v| = (-9i -12j)/15
u = -0.6i -0.8j
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Additional comment
The attached calculator output shows the polar form angle as negative. That is another way the direction can be expressed. The positive angle value is found by adding 360° to that negative value.