Two equal force act at a point. The square of their resultant is 3 times their product. Find the angle between them.

Two equal forces have their resultant equal to either. What is the inclination between them?

The difference of squares of two numbers is 180.The square of the smaller number is 8 times the larger number.Find the two numbers.

If resultant of two vectors of equal magnitude is equal to the magnitude of either vector what is the angle between them?

The electric field produced due to an electron is just sufficient to balance the gravitational force on another electron located above the first. Find the distance between the two electrons.

The dot product of two vectors of magnitudes 4 units and 5 units is 10 units in magnitude . Find the angle between them.

Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46,find the integers.

Two pillars of equal height stand on either side of a road which is 150m wide. At a point on the road between the pillars the angle of elevation of the top of the pillars are 60° and 30°. Find the height of each pillar and the position of the point on the road.

To draw a pair of tangents to a circle which are inclined to each other at an angle of 60° it is required to draw tangents at end point of these radii of the circle. The angle between them is

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the bisectors of the corresponding angles of the triangles. [The end-points of the angular bisectors are on the opposite sides of the angles.]