The equation of the plane passing through the line of intersection of the planes vecrcdot (hati+hatj+hatk )=1 and vecrcdot (2hati+3hatj-hatk )+4=0 and parallel to the x -axis is :

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

JEE Main 2021 (Online) 27th August Evening ShiftQuestion 1

The equation of the plane passing through the line of intersection of the planes $\vec{r}\cdot\left(\hat{i}+\hat{j}+\hat{k}\right)=1$ and $\vec{r}\cdot\left(2\hat{i}+3\hat{j}-\hat{k}\right)+4=0$ and parallel to the $x$-axis is :

3D Geometry

$\vec{r}\cdot\left(\hat{i}-3\hat{k}\right)+6=0$$\vec{r}\cdot\left(\hat{i}+3\hat{k}\right)+6=0$$\vec{r}\cdot\left(\hat{j}-3\hat{k}\right)-6=0$$\vec{r}\cdot\left(\hat{j}-3\hat{k}\right)+6=0$✓ Correct answer

Solution

Plane $(x+y+z-1)+\lambda(2x+3y-z+4)=0$ parallel to $x$-axis: coefficient of $x$ is $1+2\lambda=0$, $\lambda=-\frac12$, giving $-y+3z-6=0$, i.e. $\vec r\cdot(\hat j-3\hat k)+6=0$.

3D Geometry - JEE Mathematics question (JEE Main 2021 (Online) 27th August Evening Shift)

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