Write the cartesian and vector equations of z-axis. - Vidyadip

Question

Write the cartesian and vector equations of z-axis.

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Answer

Since z-axis passes through the point (0, 0, 0) having position vector $\vec{\text{a}}=0\hat{\text{i}}+0\hat{\text{j}}+0\hat{\text{k}}$ and is parallel to the vector $\vec{\text{b}}=0\hat{\text{i}}+0\hat{\text{j}}+\hat{\text{k}}$ having direction ratios proportional to 0, 0, 1, the cartesian equation of z-axis is
$\frac{\text{x}-0}{0}=\frac{\text{y}-0}{0}=\frac{\text{z}-0}{1}$
$=\frac{\text{x}}{0}=\frac{\text{y}}{0}=\frac{\text{z}}{1}$
Also, its vector equation is
$\vec{\text{r}}=\vec{\text{a}}+\lambda\vec{\text{b}}$
$=0\hat{\text{i}}+0\hat{\text{j}}+0\hat{\text{k}}+\lambda\big(0\hat{\text{i}}+0\hat{\text{j}}+\hat{\text{k}}\big)$
$=\lambda\hat{\text{k}}$

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