Write the Cartesian and vector equations of Z-axis.

Explanation

As we see here Z-axis passes through the point (0, 0, 0).

Then the position Vector `vec{a}=0hat{i}+0hat{j}+0hat{k}`

Since, it is also parallel to the vector,
`vec{b}=0hat{i}+0hat{j}+hat{k}` having direction ratios proportional to 0, 0, 1, the Cartesian equation of z-axis is

`(x-0)/0=(y-0)/0=(z-0)/1`

Also, its vector equation is

`vec{r}=vec{a}+\lambda vec{b}`

`vec{r}=0hat{i}+0hat{j}+0hat{k}+\lambda0hat{i}+0hat{j}+hat{k}`

`=lambda\hat{k}`