Vector question?

Vector A has magnitude 4.0 m and points to the right; vector B has magnitude 3.0 m and points vertically upward. A is vector A, B is vector B, C is vector C.





1. Find the magnitude of a vector C such that A+B+C=0.





Answer: 5.0 m





2. find the direction of C, such that A+B+C=0





Answer is in units 'degrees counterclockwise from A'.











Will you please help me? I can't figure this out. I've tried making it into a right triangle and using proportions like 5/sin90=3/sinx. It says that answer is not correct.

Vector question?
1. Find the magnitude of a vector C such that A+B+C=0.





A = %26lt;4, 0%26gt;


B = %26lt;0, 3%26gt;





A + B + C = 0


C = -A - B = -%26lt;4, 0%26gt; - %26lt;0, 3%26gt; = %26lt;-4, -3%26gt;





Calculate the magnitude of C.





|| C || = √[(-3)² + (-4)²] = √(9 + 16) = √25 = 5





2. Find the direction of C, such that A+B+C=0





Let θ be the angle formed by vector C with the positive x-axis in a counterclockwise direciton.





tanθ = -3/(-4) = 3/4





θ = arctan(3/4) + 180° ≈ 216.9°





Note: Since both the x and y components of C are negative, θ is in the third quadrant. Since the arctan of a positive number is in the first quadrant we needed to add 180°.
Reply:The first one is easy. The vectors form a right triangle with sides 3 and 4. By Pythag. theorem, vector C has a magnitude of 5.0 m.





For the second, we just use trigonometry to find the angle.





tanx = 3/4


x = arctan(3/4)


x = 36.9 degrees





So Vector C = 5.0 m [36.9 degrees CCW from A]