If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points `(a^2+1,a^2+1)` and `(2a ,-2a),` then find the orthocentre.

If the circumcentre of a triangle lies at the point (a, a) and the centroid is the mid - point of the line joining the points (2a+3, a+4) and (a-4, 2a-3) , then the orthocentre of the triangle lies on the line

Statement-1: If the circumcentre of a triangle lies at origin and centroid is the middle point of the line joining the points (2,3) and (4,7), then its orthocentre satisfies the relation 5x-3y=0 Statement-2: The circumcentre, centroid and the orthocentre of a triangle is on the same line and centroid divides the lines segment joining circumcentre in the ratio 1:2

Find the distance of the point (1,-2,3) from the line joining the points (-1,2,5) and (2,3,4).

Find the distance of the point (1,2) from the mid-point of the line segment joining the points (6,8) and (2,4)

If point P(4,2) lies on the line segment joining the points A(2,1) and B(8,4) then :

If point P(4,2) lies on the line segment joining the points A(2,1) and B(8,4) then

Find the angle between the lines Joining the points (-1,2),(3,-5) and (-2,3),(5,0)

if the straight line joining the points (3,4) and (2,-1) be parallel to the line joining the points (a,-2) and (4,-a), find the value of a.

Find the angle between the line joining the points (1,-2), (3,2) and the line x+2y-7=0

A point with z-coordinate 6 lies on the line segment joining the points (2, 1, 2) and (6, 0, 8). Find the coordinates of the point.