List of top Mathematics Questions on Plane asked in JEE Main

Let the plane $P : 8 x+\alpha_1 y+\alpha_2 z+12=0$ be parallel to the line $L : \frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}$. If the intercept of $P$ on the $y$-axis is 1 , then the distance between $P$ and $L$ is :

A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\prime}$, to the $y$-axis at $45$ and to the $z$-axis at an acute angle If a plane passing through the points $(\sqrt{2},-1,1)$ and $(a, b, c)$, is normal to $\vec{v}$, then
A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\prime}$, to the $y$-axis at $45$ and to the $z$-axis at an acute angle If a plane passing through the points $(\sqrt{2},-1,1)$ and $(a, b, c)$, is normal to $\vec{v}$, then
Let $P$ be the plane, passing through the point $(1,-1,-5)$ and perpendicular to the line joining the points $(4,1,-3)$ and $(2,4,3)$. Then the distance of $P$ from the point $(3,-2,2)$ is
If the equation of the plane passing through the point $(1,1,2)$ and perpendicular to the line $x-3 y+$ $2 z-1=0=4 x-y+z$ is $A t+ B y+ C z=1$, then $140( C - B + A )$ is equal to______
Let \(P1:\overrightarrow{r}.(2\^i+\^j−3\^k )=4\) be a plane. Let \(P_2\) be another plane which passes through points  \((2, - 3, 2)\), \((2, - 2, -3)\) and \((1, -4, 2)\). If the direction ratios of the line of intersection of \(P_1\) and \(P_2\) be \(16, α,β,\) then the value of \(α + β\) is equal to _____ .
The length of the projection of the line segment joining the points $ (5, -1, 4)$ and $(4, -1, 3)$ on the plane, $x + y + z = 7$ is: