Question

Write the cartesian and vector equations of Z-axis.

Answer 1

Since z-axis passes through the the point (0, 0, 0) having position vector $\overrightarrow{a}=0\hat{i}+0\hat{j}+0\hat{k}$ and is parallel to the vector $\overrightarrow{b}=0\hat{i}+0\hat{j}+\hat{k}$ having direction ratios proportional to 0, 0, 1, the cartesian equation of z-axis is

$$\begin{gathered} \frac{x-0}{0}=\frac{y-0}{0}=\frac{z-0}{1} \\ =\frac{x}{0}=\frac{y}{0}=\frac{z}{1} \end{gathered}$$

Also, its vector equation is

$$\begin{gathered} \overrightarrow{r}=\overrightarrow{a}+\lambda \overrightarrow{b} \\ =0\hat{i}+0\hat{j}+0\hat{k}+\lambda \left(0\hat{i}+0\hat{j}+\hat{k}\right) \\ =\lambda \hat{k} \end{gathered}$$