NEET-XII-Physics
02: Physics and Mathematics
- #4Can you add three unit vectors to get a unit vector? Does your answer change if two unit vectors are along the coordinate axes?Ans : Yes we can add three unit vectors to get a unit vector.
No, the answer does not change if two unit vectors are along the coordinate axes. Assume three unit vectors `` \vec{i,}-\vec{i}\mathrm{and}\vec{j}`` along the positive x-axis, negative x-axis and positive y-axis, respectively. Consider the figure given below:
The magnitudes of the three unit vectors (`` \vec{i,}-\vec{i}\mathrm{and}\vec{j}`` ) are the same, but their directions are different.
So, the resultant of `` \vec{i}\mathrm{and}-\vec{i}`` is a zero vector.
Now, `` \vec{j}+\stackrel{\to }{0}=\vec{j}`` (Using the property of zero vector)
∴ The resultant of three unit vectors (`` \vec{i,}-\vec{i}\mathrm{and}\vec{j}``) is a unit vector (`` \vec{j}``).
Page No 28: