Step-by-step explanation:
1. A+B=Just add the J hat with J hat and add the I hat with the I hat.
[tex](3i + ( - 1)i + ( - 2) + ( - 4)j = 2i - 6j[/tex]
A-B=
[tex]3 - ( - 1)i + ( - 2) - ( - 4)j = 4i + 4j[/tex]
2. Take the magnitude of A+B
[tex]2 {}^{2} + ( - 6) {}^{2} = {r}^{2} [/tex]
[tex]40 = {r}^{2} [/tex]
[tex]r = \sqrt{40} [/tex]
So the magnitude is root of 40.
So the magnitude of A+B is
The magnitude of A-B
[tex] {4}^{2} + {4}^{2} = 4 \sqrt{2} [/tex]
So the magnitude is
[tex]4 \sqrt{2} [/tex]
c. To find direction, we need to find the angle.
Use this rule,
[tex] \tan(x) = \frac{bj}{bi} [/tex]
For A+B, we get
[tex] \tan(x )= \frac{ - 6}{2} [/tex]
[tex] \tan(x) = - 3[/tex]
Since this is a southeast, the degree is 288.43.
The direction is southeast, 288.43 degrees
For A-B, we get
[tex] \tan(x) = \frac{4}{4} [/tex]
[tex] \tan(x) = 1[/tex]
Since this is northeast, the degree is 45 degrees.
The direction is northeast, 45 degrees.
