Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Is the Vector Sum of the Unit Vectors → I and → I a Unit Vector? If No, Can You Multiply this Sum by a Scalar Number to Get a Unit Vector? - Physics

Is the vector sum of the unit vectors  $\vec{i}$ and $\vec{i}$ a unit vector? If no, can you multiply this sum by a scalar number to get a unit vector?

#### Solution

No, the vector sum of the unit vectors $\vec{i}$ and  $\vec{i}$  is not a unit vector, because the magnitude of the resultant of $\vec{i}$ and $\vec{j}$ is not one.
Magnitude of the resultant vector is given by
R = $\sqrt{1^2 + 1^2 + \cos90^\circ} = \sqrt{2}$

Yes, we can multiply this resultant vector by a scalar number $\frac{1}{\sqrt{2}}$ to get a unit vector.

Concept: What is Physics?
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 2 Physics and Mathematics
Short Answers | Q 10 | Page 28
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