Question

Let ε1 and ε2 be the angles made by →A and -→A with the positive X-axis. Show that tan ε1 = tan ε2. Thus, giving tan ε does not uniquely determine the direction of →A.

Answer 1

Explanation:

• The -$-A \rightarrow^{\prime} S$ direction is opposite to $A \rightarrow$. So, if the angles $\mathcal{E}_{2}$ and $\mathcal{E}_{1}$ are made by the vectors $-A \rightarrow$ and $A \rightarrow$ with the X-axis, respectively, then ε2 is equal to ε1 as displayed in the figure:

• Here, tan $\varepsilon_{2}=\tan \varepsilon_{1}$

• This is due to the reason that these are alternative angles.

• Thus, the direction of $A \rightarrow$ is not uniquely determined by $\tan \varepsilon$.

• Hence, it is proved that $\tan \varepsilon_{2}=\tan \varepsilon_{1}$.