O is the origin and A is (a,b,c). Find the d.c. of OA and the equation of the plane through A at right angles of OA.

Find the differential equation of the family of lines through the origin.

If O be 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.

A variable plane passes through a fixed point a,b,c and meet the co-ordinates axes in A,B,C. Show that the locus of the point common to the planes through A,B,C parallel to the co-ordinate planes is a/x+b/y+c/z=1

Find the equation of the plane passing through origin and parallel to the plane x+3y-2z+7=0 .

Fill ups A plane 'p' passes through the point P(1,-2,3). If O is the origin and OPbotp , then equation of the plane p is………….. .

OABCDE is a regular hexagon of side 2 units in the XY-plane in the first quadrant. O being the origin and OA taken along the x-axis. A point P is taken on a line parallel to the z-axis through the centre of the hexagon at a distance of 3 units from O in the positive Z direction. Then find vector vec(AP) .

If a circle of constant radius 3k passes through the origin and meets the axes at Aa n dB , prove that the locus of the centroid of triangle OA B is a circle of radius 2cdot

Let O A C B be a parallelogram with O at the origin and O C a diagonal. Let D be the midpoint of O Adot using vector methods prove that B Da n dC O intersect in the same ratio. Determine this ratio.

Let 2x^2 + y^2- 3xy = 0 be the equation of a pair of tangents drawn from the origin O to a circle of radius 3 with centre in the first quadrant. If A is one of the points of contact, find the length of OA.

Let 2x^(2)+y^(2)-3xy=0 be the equation of a pair of tangents drawn from the origin O to a circle of radius 3 with centre in the firs quadrant. If A is one of the points of contact, find the length of OA.