Prove that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.

Three coinitial vectors of magnitudes a, 2a and 3a meet at a point and their directions are along the diagonals if three adjacent faces if a cube. Determined their resultant R. Also prove that the sum of the three vectors determinate by the diagonals of three adjacent faces of a cube passing through the same corner, the vectors being directed from the corner, is twice the vector determined by the diagonal of the cube.

Prove that the locus of the point that moves such that the sum of the squares of its distances from the three vertices of a triangle is constant is a circle.

The locus of a point which moves such that the sum of the square of its distance from three vertices of a triangle is constant is a/an (a)circle (b) straight line (c) ellipse (d) none of these

Find the position vector of the centroid of a triangle when the position vectors of the vertices are given.

How is the direction of vector product determined ?

Find the vector sum of three vectors vecA, vecB and vecC, using analytical method.

Prove by vector method that median to the base of an isoscels triangle is perpendicular to the base.

The sum of the three vectors shown in figure is zero. Find the magnitudes of the vectors vec(OB) and vec(OC) .

Name the circle which passes through three vertices of a triangle.

Prove that second derivative of position vector is not zero then there must be a force on the body