Question 2: The magnitudes of three vectors are 2 cm, 3 cm and 5 cm, respectively. The directions are at your disposal. Can these vectors be added to yield zero? Illustrate with a diagram.
Yes, vectors of 2 cm, 3 cm and 5 cm can be added to yield a zero resultant. We use geometrical method of vector addition to prove the assertion.
Take a line of 2 cm length with A and B as end points as shown in the diagram. Now open the compass 3 cm wide. Take point B as center, draw an arc. All points on this arc are at 3 cm distance from point B.
Now open the compass 5 cm and draw another arc with point A as center. Let the two arcs meet at point C.
Now point C is at a distance of 3 cm from point B and 5 cm from point A. Meet C with A and B. AC is 5 cm and BC is 3 cm.
Let AB, BC and CA are vectors as shown in the figure. We see it is three vectors added by head-to-tail rule with zero resultant.
This proves the statement.