Question

A particle moves 3 m due east, then it moves 4 m
due north. How many unit vectors (S.I. unit) are there
in its displacement ?​

Answer 1

Your Answer:

Let O be the point where the particle starts it journey.

And OA be the point where the particle moves 3m due east.

And AB be the point where the particle moves 4m due north.

To Find:-

• How many unit vectors are there in the displacement of the particle from the starting point to the end point.

From figure, it is clear that we have to find OB

So, to find OB we have to apply Pythagoras Theorem in the OAB triangle.

So,

$\tt OB^2=OA^2+AB^2$

Where

$\tt \blacktriangleright OA=\overrightarrow{3m} \\\\ \tt \blacktriangleright AB = \overrightarrow{4m}$

So, finding OB

$\tt OB^2 = (3m)^2+(4m)^2 \\\\ \tt \Rightarrow OB^2= 9m^2+16m^2 \\\\ \tt \Rightarrow OB^2 = 25m^2 \\\\ \tt \Rightarrow OB = \sqrt{25m^2} \\\\ \tt \Rightarrow OB =5m$

So, 5m is the unit displacement of the particle.

5 meter vector is the answer.