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Question
Write the cartesian and vector equations of Z-axis.
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Solution
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
\[\frac{x - 0}{0} = \frac{y - 0}{0} = \frac{z - 0}{1}\]
\[ = \frac{x}{0} = \frac{y}{0} = \frac{z}{1}\]
Also, its vector equation is ,
\[\overrightarrow{r} = \overrightarrow{a} + \lambda \overrightarrow{b} \]
\[ = 0 \hat{i} + 0 \hat{j} + 0 \hat{k} + \lambda\left( 0 \hat{i} + 0 \hat{j} + \hat{k} \right)\]
\[ = \lambda \hat{k} \]
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