## Question 1: Is it possible to add three vectors of equal magnitudes but different directions to get a null vector? Illustrate with a diagram.

A closed shape may be thought of as sum of vectors with zero resultant vector. Therefore, if three vectors of equal magnitudes and different directions form a closed shape, then their resultant is a null vector. Therefore, it is possible to combine three vectors of equal magnitudes and different directions to give a null vector as their resultant.

#### Illustration

Take a line of 4 cm as shown in the figure below. The end points of the vector line are A and B. Now take a compass and open it 4 cm wide. With point A considering as center, draw an arc of suitable length. Every point on this arc is at a distance of 4 cm from point A. Again draw another arc with point B as center in such a way that it meets with the first arc at point C. All points on this arc are also at a distance of 4 cm from point B.

Now the point of intersection of the two arcs is at a distance of 4 cm both from point A and B. Meet point C with points A and B. Distance BC and distance AC are both 4 cm.

Now we have a triangle (closed shape) with the three sides AB, BC and CA all 4 cm. If AB is considered vector a, BC as vector b and CA as vector c, then the resultant of the three is zero. It is because the head of vector c meets with the tail if vector a. So three vectors of same magnitude and different directions may be combined together to give null vector.