Show that the area of the triangle contained between the vectors a and b is one half of the magnitude of `a × b`.

Prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangles described on its diagonal.

Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

Show that the median of a triangle divides it into two triangles of equal areas.

When the angle between two vectors of equal magnitudes is 2/3, prove that the magnitude of the resultant is equal to either.

In triangle ABC, a = 4 and b = c = 2 sqrt(2) . A point P moves within the triangle such that the square of its distance from BC is half the area of rectangle contained by its distance from the other two sides. If D be the centre of locus of P, then

The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B. Then the angle between A and B is

The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B . Then the angle between A and B is : (a) 30^(@) (b) 45^(@) (c) 150^(@) (d) 120^(@)

When is the magnitude of (A+B) equal to the magnitude of (A-B)?

Find the area of the triangle whose adjacent sides are made by the vectors vec a = 3 hat i + 4 hat j + 4 hat k and vec b = hat i - hat j + hat k .