Answer:
[tex]\vec{B}=-3\hat{i}+1\hat{j}[/tex]
Explanation:
given,
[tex]\vec{C} = 3 i + 4 j[/tex]
magnitude of vector C
[tex] C = \sqrt{3^2+4^2}[/tex]
[tex] C = 5 [/tex]
Sum of vector B and vector C is equal to magnitude of vector C in y-direction
[tex]\vec{B}+\vec{C} = 5\hat{j}[/tex]
[tex]\vec{B}+( 3\hat{i}+4\hat{j})= 5\hat{j}[/tex]
now, vector B is equal to
[tex]\vec{B}=5\hat{j} - ( 3\hat{i}+4\hat{j})[/tex]
[tex]\vec{B}=-3\hat{i}+1\hat{j}[/tex]
Hence, the given vector B is equal to [tex]\vec{B}=-3\hat{i}+1\hat{j}[/tex]
