List of top Mathematics Questions on Plane asked in AP EAMCET

If the plane \[ x - y + z + 4 = 0 \] divides the line joining the points \[ P(2,3,-1) \quad {and} \quad Q(1,4,-2) \] in the ratio \( l:m \), then \( l + m \) is:

Let \( P(x_1, y_1, z_1) \) be the foot of the perpendicular drawn from the point \[ Q(2, -2, 1) \] to the plane \[ x - 2y + z = 1. \] If \( d \) is the perpendicular distance from the point \( Q \) to the plane and \[ I = x_1 + y_1 + z_1, \] then \( I + 3d^2 \) is:

The \(x\)-intercept of a plane \(\pi\) passing through the point \((1,1,1)\) is \(\dfrac{5}{2}\) and the perpendicular distance from the origin to the plane \(\pi\) is \(\dfrac{5}{7}\). If the \(y\)-intercept of the plane \(\pi\) is negative and the \(z\)-intercept is positive, then its \(y\)-intercept is

When the coordinate axes are rotated about the origin in the positive direction through an angle $\frac{\pi}{4}$, if the equation $25 x^2 + 9y^2 = 225$ is transformed to $\alpha x^2 + \beta xy + \gamma y^2 = \delta$, then $(\alpha + \beta + \gamma - \sqrt{\delta})^2$ =