When the axes are rotated through an angle `60^(@)` ,the new coordinates of the point are `(-7,2)` , if its original coordinates are `(alpha, beta)` then
`(2)/(53)(-7 alpha+2 beta)=`

If the axes are rotated through an angle 45^(@) and the point P has new coordinates (2sqrt(2),sqrt(2)) then original coordinates of

If the axes are rotated through an angle (pi)/(4) and the point P has new coordinates (2sqrt(2),sqrt(2)) ,then original coordinates of P are

If the axes are rotated through an angle of 45^(@) in the clockwise direction, the coordinates of a point in the new systeme are (0,-2) then its original coordinates are

If origin is shifted to the point (2,3) and the axes are rotated through an angle pi//4 in the anticlokwise direction, then find the coordinates of the point (7, 11) in the new system of coordinates.

If (2,3) are the coordinates of a point Pin the new system when the origin is shifted to (-3, 7) then the original coordinates of P are

If (2,3) are the coordinates of a point P in the new system when the origin is shifted to (-3,7) then the original coordinates of P are

If (cos alpha,cos beta) are the new co-ordinates of a point P when the axes are translated to the point (1,1), then the original coordinates are

Keeping the origin constant axes are rotated at an angle 30^@ in anticlockwise direction then new coordinate of (2, 1) with respect to old axes is

A variable plane is at a constant distance 3p from the origin and meets the coordinates axes in A,B and C if the centroid of triangle ABC is (alpha,beta,gamma ) then show that alpha^(-2)+beta^(-2)+gamma^(-2)=p^(-2)