The vector equation of the plane passing through the intersection of the planes vecrcdot (hati+hatj+hatk )=1 and vecrcdot (hati-2hatj )=-2 , and the point (1,0,2) is :

vecrcdot (3hati+7hatj+3hatk )=7

vecrcdot (hati-7hatj+3hatk )=(7)/(3)

vecrcdot (hati+7hatj+3hatk )=(7)/(3)

3D Geometry: The vector equation of the plane passing through the intersection of… | JEE Main 2021

JEE Main 2021 (Online) 24th February Evening ShiftQuestion 1

The vector equation of the plane passing through the intersection of the planes $\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=1$ and $\vec{r}\cdot\left(\hat{i}-2\hat{j}\right)=-2$, and the point $(1,0,2)$ is :

3D Geometry

$\vec{r}\cdot\left(3\hat{i}+7\hat{j}+3\hat{k}\right)=7$$\vec{r}\cdot\left(\hat{i}+7\hat{j}+3\hat{k}\right)=7$✓ Correct answer$\vec{r}\cdot\left(\hat{i}-7\hat{j}+3\hat{k}\right)=\frac{7}{3}$$\vec{r}\cdot\left(\hat{i}+7\hat{j}+3\hat{k}\right)=\frac{7}{3}$

Solution

Family $(x+y+z-1)+\lambda(x-2y+2)=0$ through $(1,0,2)$: $2+3\lambda=0$, $\lambda=-\frac23$. This gives $x+7y+3z=7$, i.e. $\vec r\cdot(\hat i+7\hat j+3\hat k)=7$.

3D Geometry - JEE Mathematics question (JEE Main 2021 (Online) 24th February Evening Shift)

More from 3D Geometry