Question

two vectors are defined as follows: A= (-2.2m)x and B = (1.4m)y. (a) Is the magnitude of 1.4 A greater than, less than or equal to the magnitude of 1.2B? (b) Is the x component of 1.4A greater than, less than or the same as the y component of 2.2B?

Answer 1

We are given the following two vectors

`\begin{gathered} \vec{A}=(1.4\; m)\hat{x} \\ \vec{B}=(-2.2\; m)\hat{y} \end{gathered}`

(a) The magnitude of vector A (1.4 m) is less than the magnitude of vector B (2.2 m) because the absolute value of vector A (1.4 m) is less than the absolute value of vector B (-2.2 m)

`\begin{gathered} |\vec{A}|=|1.4|=1.4\; m \\ |\vec{B}|=|-2.2|=2.2\; m \end{gathered}`

(b) The x component of vector A (1.4 m) is greater than the y component of vector B (-2.2 m) because the x component of vector A (1.4 m) is positive as compared to the y component of vector B (-2.2 m)