Use unit vectors to express the vector C, where C = 3.00 A - 4.00 B?

Question

Use unit vectors to express the vector C, where C = 3.00 A - 4.00 B

I figured out some of the problem I found A to equal 1.41i + 3.31 j and I found B to equal -2.08i + -1.2 j

* but I cant figure out how to find C, and once I find Vector C's i and j, I then need to find the magnitude and direction of C.......... Lost, Phsyics is hard,

* in repsonse to first answer* nope it is what I said, its an online quiz Im rather confused my self, I was given a diagrham with 2 angles and two lines with meter lengths and told to find the i and j of both A and B and then figure out the i and j of C with C: 3.00a -4.00B I have no idea

Answer 1

Assuming i is x axis and j is y axis,
A = (1.41, 3.31)
B = (-2.08, -1.2)
C = 3A + 4B = ( 4.23, 9.93) + (-8.32, -4.8) = (-4.09, 5.13)
Magnitude = 6.561
Angle = atan2(-4.09, 5.13) = 128.564 deg
Note atan2 is like the arctan function but gives angles in all 4 quadrants rather than only quadrants 1 & 4.
Expressed in unit vector form:
unit(C) = (-4.09, 5.13)/6.561 = (-0.6234, 0.7819)
(Vector (-0.6234, 0.7819) has a magnitude of 1)
C = mag(C) * unit(C) = 6.561*(-0.6234, 0.7819)

Answer 2

Uh..are you sure the book or problem is refering A as "i" and B as "j"?
Then the vector of C would be <3,-4>

Magnitude= √(3)^2 + (-4)^2
= 5

Answer 3

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Answer 4

Informative discussion, just what I was searching for.