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  4. The direction of vector vec A is reversed. What are the values Δ vec A and Δ| vec A | ?

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Q. The direction of vector $\vec{ A }$ is reversed. What are the values $\Delta \vec{ A }$ and $\Delta|\vec{ A }| ?$

Jharkhand CECEJharkhand CECE 2004Motion in a Plane

Solution:

When direction of a vector is reversed it has same magnitude but -with minus sign.
The value of $\Delta \vec{A}=\vec{A}_{2}-\vec{A}_{1}$
Given, $\vec{A}_{1}=, A, \vec{A}_{2}=-A $
$\therefore $ $\Delta \vec{A}=-A-A=-2 \vec{A}$
Also, $|\vec{A}|=|-\vec{A}| $
$\therefore \Delta|\vec{A}|=0$