Answer to Question #2651 in Mechanics | Relativity for tom

Question

A vector R = B + C . If the vector C = 3i + 4 j and vector R has a magnitude equal to that of vector C and it is in positive y direction and what is the magnitude and direction of vector B ?

Answer 1

Notice that the length of C is √(3²+4²)=5.
By assumption the length of R is also 5. Since R is in positive y direction, it follows that R=5j, whence B = R-C = (0-3)i + (5-4)j = -3i+j