Three Dimensional Geometry — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsThree Dimensional Geometry2 Marks
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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