Question

Consider the two vectors A with arrow = 3 î − ĵ and B with arrow = − î − 4 ĵ.
(a) Calculate A with arrow + B with arrow
î +
ĵ

(b) Calculate A with arrow − B with arrow
î +
ĵ

(c) Calculate

A with arrow + B with arrow




(d) Calculate

A with arrow − B with arrow




(e) Calculate the directions of A with arrow + B with arrow and A with arrow − B with arrow.
A with arrow + B with arrow
° (counterclockwise from the +x axis)
A with arrow − B with arrow
° (counterclockwise from the +x axis)

Answer 1

a)

$$\vec A+\vec B=(3 î − ĵ )+(− î − 4 ĵ)=2 î − 5ĵ$$

b)

$$\vec A-\vec B=(3 î − ĵ )-(− î − 4 ĵ)=4 î +3ĵ$$

c)

$$|\vec A+\vec B|=\sqrt{2^2+(-5)^2}=\sqrt{29}\approx 5.4$$

d)

$$|\vec A-\vec B|=\sqrt{4^2+(3)^2}=5$$

e)

$$\theta_+=360\degree-\arctan\frac{5}{2}=291.8\degree$$

$$\theta_-=\arctan\frac{3}{4}=36.9\degree$$