Analytic Geometry Answers

Show that the points (2,0,1),(0,4,-3) and
(-2,5,0) are non-collinear.Hence find the equation of plane passing through them.

Two equal concurrent forces, each of F N have a resultant of 6 N. When the magnitude of one of the forces is doubled, the resultant becomes 11 N. Calculate the value of F and the angle between the forces.

If the tangents at two points of a parabola are at right angles, then show that they intersect at a point on the directrix.

Let y^2=4ax be a parabola and p be a point on it. Let the normal at p intersects the x-axis at Q. Draw a line at Q perpendicular to the above normal. Show that the line intersects the parabola y^2+4a(x-2a)=0

If normal at one extremity of latus rectum of an ellipse passes through one extremity of minor axis, prove that the eccentricity e is given by e^4+e^2,-1=0

In a parabola show that the tangent at any point makes equal angles with the foci radius of the point and the line parallel to the x-axis through the point

Given r= -i+2j+2k, find the magnitude of r

The line with equation x+3y=6 cuts the x axis at A the y axis at B .Find the equation of (I) median from origin to AB. (II) median from A to OB. (III) median from B to OA

If
α=3i−j+2k,

β=2i+j−k and
,
γÌ…=i−2j+2k, find

α×β×γ.