If in a triangle ABC; AD, BE and CF are the altitudes and R is the circum-radius, then the radius of the circle DEF is -

In an equilateral triangle of side cms, the circum radius is -

The circumradius is 2cm.

If the lines and are concurrent then

is a unit vector such that 0 then a unit vector perpendicular to

The reflection of the point (2, –1, 3) in the plane 3x – 2y – z = 9 is :

A, B, C & D are four points in a plane with position vectors respectively such that Then for the triangle ABC, D is its:

Equation of the angle bisector of the angle between the lines

The sine of angle formed by the lateral face ADC and plane of the base ABC of the tetrahedron ABCD where A º (3, –2, 1) ; B º (3, 1, 5); C º (4, 0, 3) and D º (1, 0, 0) is -

Four coplanar forces are applied at a point O. Each of them is equal to k and the angle between two consecutive forces equals 45º as shown in the figure. Then the resultant has the magnitude equal to :

be vectors of length 3,4,5 respectively. be perpendicular to and is equal to :

and is equal to :

If ABCDEF is a regular hexagon and if then

If is along the angle bisector of then -

If the solution of the differential equation

A curve passes through the point Let the slope of the curve at each point (x, y) be Then the equation of the curve is

The solution of the differential equation