**Question 1:** Explain with the help of example, what is the range of possible values of the resultant of two vectors.

Answer

When two scalar quantities are added, they always give the same result or one value. For example, 2 kg and 2 kg when added will always give 4 kg. The case of vector quantities is different, however.

Vectors are directional quantities. Their sum depends on their relative directions to one another, that is, the angle between them. The value of the sum of same vectors may be different for different angles. The range of possible values of the resultant vectors varies between the maximum and minimum values obtained by the addition of two vectors. The maximum and minimum values of the sum depend upon the range of angels they make with one another.

Let’s consider two vectors and , as shown in the figure. If both vectors are acting along the same direction, their resultant is maximum. When the two vectors are acting anti-parallel ( = – ), their resultant vector is minimum. Therefore, the range of possible values of the resultants of and will lie between + and – .

Therefore, is the possible range of the resultant of the two vectors.

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