Question

If $\vec{B}$ is added to $\vec{C}$ , the result is a vector in the direction of the positive y-axis with a magnitude equal to that of $\vec{C}$ . If $\vec{C}=2.75\hat{i}+3.66\hat{j}$ , what is the magnitude of $\vec{B}$ ? Answer should be in 3 significant figures.

Answer 1

First you need to find what's the magnitude of C,

Mc = sqrt(x^2 +y^2) = sqrt(2.75^2 +3.66^2) = 4.578

In order to have the same magnitude and be in the y axis the resulting vector must be equal to 4.578j.

Finally you solve for B.
B + C = 4.578j
B + 2.75i + 3.66j = 4.578j
Answer: B = -2.75i + 0.918j