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Define unit vector and give its physical significance. |
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Answer» Unit vector: A vector having unit magnitude in a given direction is called a unit vector in that direction. If \(\overset\rightarrow{p}\) is a non zero vector (P ≠ 0) then the unit vector \(\hat{u}_p=\frac{\overset\rightarrow{P}}{P}\) ∴ \(\overset\rightarrow{p}=\hat{u}_p\,P\) Significance of unit vector: i. The unit vector gives the direction of a given vector. ii. Unit vector along X, Y and Z direction of a rectangular (three dimensional) coordinate is represented by \(\hat{i}\), \(\hat{j}\) and \(\hat{K}\) respectively Such that \(\hat{u}_x=\hat{i}\), \(\hat{u}_y=\hat{j}\) and \(\hat{u}_z=\hat{K}\) This gives \(\hat{i}=\frac{\overset\rightarrow{X}}{X}\), \(\hat{j}=\frac{\overset\rightarrow{Y}}{X}\) and \(\hat{K}=\frac{\overset\rightarrow{Z}}{Z}\) |
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