A water jet from the fountain reaches its maximum height of 4 metres at a distance of 0.5 metre from the vertical passing through the point A of the water outlet. Show that the height of the jet above the horizontal AX at a distance of 0.75 metre from the point A is 3 metres.

Find the distance of (-1,2,5) from the plane passing through the point (3,4,5) whose direction ratios are .

Find the value of x, so that the point (6,5,-3) is at a distance of 13 units from the point (x,-7,0).

The angle of elevation of the top of a tower from a point A on the ground is 30^@ . On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60^@ . Find the height of the tower and distance of the tower from the point A.

Find the direction in which a straight line must be drawn through the point (-1, 2) so that its point of intersection with the line x+y= 4 may be at a distance of 3 units from this point.

Find the points on the line through the points A(1,2,3) and B(5,8, 15) at a distance of 14 units from the mid point of AB.

The distance of the plane 2x-y+2z+3=0 from the point (3,2,1) is

Find the direction in which a straight line must be drawn through the point (-1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

A bridge is in the shape of a semi-ellipse. It is 400 metres One and has a maximum height of 10 metres at the middle point. The height of the bridge at a point distant 80 metres from one end is :

A tent is of the shape of a right circular cylinder upto height of 3 metres and then becomes a right circular cone with maximum height of 13.5 metres above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs.2 per square metre, if the radius of the base is 14 metres.