If `O` is the origin, `O P=3` with direction ratios `-1,2,a n d-2,` then find the coordinates of `Pdot`

If vec r is a vector of magnitude 21 and has direction ratios 2,-3a n d6, then find vec rdot

If the midpoints of the sides of a triangle are (2,1),(-1,-3),a n d(4,5), then find the coordinates of its vertices.

The line joining the points (-2,1,-8)a n d(a ,b ,c) is parallel to the line whose direction ratios are 6,2,a n d3. Find the values of a ,b and c

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

If from a point P , tangents P Qa n dP R are drawn to the ellipse (x^2)/2+y^2=1 so that the equation of Q R is x+3y=1, then find the coordinates of Pdot

If O is the origin and the coordinates of P be (1,2,-3) , then find the equation of the plane passing through P and perpendicular to OP.

Point A(9,12) rotates around the origin O in a plane through 60^(@) in the anticlockwise direction to a new position B. Find the coordinates of the point B.

A plane is at a distance 3 units from the origin. The direction ratios of normal to the plane are 1,-2,1. Find the vector and cartesian equation of the plane.

If point P(3,2) divides the line segment AB internally in the ratio of 3:2 and point Q(-2,3) divides AB externally in the ratio 4:3 then find the coordinates of points A and B.