List of top Mathematics Questions on Plane asked in AP EAPCET

If \((3,4,-7)\) is the foot of the perpendicular drawn from the point \((-2,3,6)\) to the plane \(\pi\), then the sum of the intercepts made by the plane \(\pi\) on the \(x\)- and \(y\)-axes is

If \(a,b,c\) are the intercepts made by the plane passing through the point \((1,2,3)\) parallel to the plane \(3x+4y-5z=0\) on \(X,Y,Z\)-axes respectively, then \(3a+b+5c=\)

If \[ -2,\ \frac{4}{3},\ -\frac{4}{5} \] are the intercepts made by a plane on \(X,Y,Z\)-axes respectively, then the direction cosines of a normal to this plane are:

Let the plane \(\pi\) pass through the point \((1,0,1)\) and perpendicular to the planes \[ 2x+3y-z=2 \] and \[ x-y+2z=1. \] Let the equation of the plane passing through the point \((11,7,5)\) and parallel to the plane \(\pi\) be \[ ax+by-z+d=0. \] Then \[ \frac{a}{b}+\frac{b}{d}= \]

If the equation of the plane which is at a distance of \(\dfrac{1}{3}\) units from the origin and perpendicular to a line whose directional ratios are \((1,2,2)\) is \[ x+py+qz+r=0 \] then \[ \sqrt{p^2+q^2+r^2}= \]

If the equation of the plane passing through the point \(A(-2,1,3)\) and perpendicular to the vector \(3\vec{i}+\vec{j}+5\vec{k}\) is \(ax+by+cz+d=0\), then \(\dfrac{a+b}{c+d}=\)

Let \(\pi\) be the plane passing through the point \((3,-3,1)\) and perpendicular to the line joining the points \[ (3,4,-1) \] and \[ (2,-1,5). \] If the equation of the plane containing the points \[ (3,4,-1),\quad (-1,2,5) \] and perpendicular to the plane \(\pi\) is \[ ax+y+cz-d=0, \] then \[ 3(a+c)= \]