A plane passes through the point `(1,1,2)` - and the normal to the plane of magnitude `3sqrt(3)` makes equal acute angles with the coordinate axes. Find the equation of the plane.

Find the vector and cartesian equations of the planes a. that passes through the point (1,0,-2) and normal to the planes is hati+hatj-hatk b. that passes through the point (1,4,6) and the normal vector to the plane is hati-2hatj+hatk .

A line with positive direction cosines passes through the point P(2, – 1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals

A ray of light is sent through the point P(1,2,3) and is reflected on the XY plane. If the reflected ray passes through the point Q(3,2,5) then the equation of the reflected ray is

The foot of the perpendicular drawn from the origin to a plane is (1,2,-3)dot Find the equation of the plane. or If O is the origin and the coordinates of P is (1,2,-3), then find the equation of the plane passing through P and perpendicular to O Pdot

Statement 1: A plane passes through the point A(2,1,-3)dot If distance of this plane from origin is maximum, then its equation is 2x+y-3z=14. Statement 2: If the plane passing through the point A( vec a) is at maximum distance from origin, then normal to the plane is vector vec adot

Let a plane pass through origin and be parallel to the line (x-1)/2=(y_3)/-1=(z+1)/-2 is such that distance between the plane and the line is 5/3 . Then equation of the plane is/are

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).