Question

State whether true or false:
Vector quantities obey laws of ordinary Algebra.

Answer 1

Vector quantities are such quantities which have both magnitude and direction. On the other hand, quantities which have only magnitude are called scalar quantities.

Complete step by step answer:
There are two types of quantities which we encounter in physics- scalars and vectors. Let us take an example of each and understand which laws of addition do they follow.
Say we have two numbers 5 & 7. If we want to add them, we do not need any special law and we add them simply. Now consider two speeds 30m/s and 50m/s. Again, since It is a scalar quantity they can be added simply and we do not have to consider their direction. Now consider two forces acting on a body say 5N to the left and 4n to the right. If we want to add them both we can’t do it just 5+4=9.
This is because vector quantities have directions and we have to consider them too while adding them. Since 5n acts on the left and 4n acts on the right, so if taking the right direction to be the positive and left direction to be negative the resultant of two vectors will be 1N towards the left. Thus, this shows us that vector quantities do not obey laws of ordinary Algebra thus, the given statement is False.

Note: There are two laws to add the vectors, they are triangle law of vector addition and parallelogram law of vector addition.