Three Dimensional Geometry — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsThree Dimensional Geometry4 Marks
Question
Find the vector equations of the coordinate planes.
✓
Answer
We have to find vector equation of coordinate planes. For xy-plane. It passes through origin and is perpendicular to z-axis, so Put $\vec{\text{a}}=0\hat{\text{i}}+0\hat{\text{j}}+0\hat{\text{k}}$ and $\vec{\text{n}}=\hat{\text{k}}$in the vector equation of plane passing through point $\vec{\text{a}}$ and perpendicular to vector $\vec{\text{n}}$ $(\vec{\text{r}}-\vec{\text{n}})\vec{\text{n}}=0$ $(\vec{\text{r}}-0\hat{\text{i}}-0\hat{\text{j}}-0\hat{\text{k}})\hat{\text{k}}=0$ $\vec{\text{r}}\cdot\vec{\text{k}}=0\ ...(\text{i})$ For xz-plane, It passes throught origin and perpendicular to y-axis, so $\vec{\text{a}}=0\hat{\text{i}}+0\hat{\text{j}}+0\hat{\text{k}}$ and $\vec{\text{n}}=\hat{\text{j}}$ Equation of xz-plane is given by $(\vec{\text{r}}-\vec{\text{a}})\vec{\text{n}}=0$ $(\vec{\text{r}}-0\hat{\text{i}}-0\hat{\text{j}}-0\hat{\text{k}})\hat{\text{j}}=0$ $\vec{\text{r}}\cdot\hat{\text{j}}=0$ For yz-plane, It passes throught origin and is perpendicular to x-axis, so $\vec{\text{a}}=0\hat{\text{i}}+0\hat{\text{j}}+0\hat{\text{k}},\vec{ \text{n}}=\hat{\text{i}}$ $(\vec{\text{r}}-\vec{\text{a}})\vec{\text{n}}=0$ $(\vec{\text{r}}-0\hat{\text{i}}-0\hat{\text{j}}-0\hat{\text{k}})\hat{\text{i}}=0$ $\vec{\text{r}}\cdot\hat{\text{i}}=0$ Hence, equation of xy, yz, zx-plane are given by $\vec{\text{r}}\cdot\vec{\text{k}}=0$ $\vec{\text{r}}\cdot\hat{\text{i}}=0$ $\vec{\text{r}}\cdot\hat{\text{j}}=0$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.