The magnitude of the $x$-component of vector $\vec{A}$ is 3 and the magnitude of vector $\vec{A}$ is

Question

The magnitude of the $x$-component of vector $\vec{A}$ is 3 and the magnitude of vector $\vec{A}$ is 5 . What is the magnitude of the $y$-component of vector $\vec{A}$ ?

Professor PC Thomas Classes · Answer

(b) : $\vec{A}=A_x \hat{i}+A_y \hat{j}$ Also $A=\sqrt{A_x^2+A_y^2}$ Here, $A=5, A_x=3 ; 	herefore 5=\sqrt{(3)^2+A_y^2}$ Squaring both sides, we get $ \  25=9+A_y^2 	ext { or } A_y=4 $