Question

consider the vectors A = (1.2m)x and B = (-3.4m)×. which of these vectors has (a) the greater x component and (b) the greater magnitude

Answer 1

We are given the following two vectors

$\begin{gathered} \vec{A}=(1.2\; m)\hat{x}\; \\ \vec{B}=(-3.4\; m)\hat{x}\; \end{gathered}$

(a) Greater x component

Vector A (1.2 m) has a greater x component as compared to vector B (-3.4 m) because vector A is positive and vector B is negative.

Vector A has a greater x component

(b) Greater magnitude

Vector B (3.4 m) has a greater magnitude as compared to vector A (1.2 m) because the absolute value of vector B is greater than the absolute value of vector A.

$\begin{gathered} |\vec{A}|=|1.2|=1.2\; m \\ |\vec{B}|=|-3.4|=3.4\; m \end{gathered}$

Vector B has a greater magnitude.