CBSE Class 11-science Answered
What do your understatnd by (1)position vector and (ii) displancment vector. Distinguish them with illustration.
Asked by rk274268 | 05 Aug, 2022, 13:19: PM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/c53d8b8174d2e26eee6c9c31ac20a68562ecddee9a7ff2.59330100f6.png)
Let us consider two locations that are shown as point A and point B
Position vector of A with respect to origin O =
= ![begin mathsize 14px style a with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/d9ede463a364dc4ae9a804b43bf4b4bf.png)
![begin mathsize 14px style stack O A with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/8445bd6abcdd6b5bd798af36a301cb6b.png)
![begin mathsize 14px style a with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/d9ede463a364dc4ae9a804b43bf4b4bf.png)
Position vector of B with respect to origin O =
= ![begin mathsize 14px style b with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/1ee88d50cc6a096c65659dea54046215.png)
![begin mathsize 14px style stack O B with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/6429ab063d5b12f9f6eb701afa9539f2.png)
![begin mathsize 14px style b with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/1ee88d50cc6a096c65659dea54046215.png)
Displacement vector from initial position A to final position B is ![begin mathsize 14px style stack A B with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/dd13d277c733f00d7fc32961362628af.png)
![begin mathsize 14px style stack A B with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/dd13d277c733f00d7fc32961362628af.png)
From vector algebra, we know that
![begin mathsize 14px style stack O A with rightwards arrow on top space plus space stack A B with rightwards arrow on top space space equals space stack O B with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/cf797261480f831f6d6e99c231d9d25d.png)
Hence , displcement vector ![begin mathsize 14px style stack A B with rightwards arrow on top space equals space stack O B with rightwards arrow on top space minus space stack O A with rightwards arrow on top space equals space b with rightwards arrow on top space minus space a with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/493ae66a7995d2b4a4f6978469ef4939.png)
![begin mathsize 14px style stack A B with rightwards arrow on top space equals space stack O B with rightwards arrow on top space minus space stack O A with rightwards arrow on top space equals space b with rightwards arrow on top space minus space a with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/493ae66a7995d2b4a4f6978469ef4939.png)
( Displacement vector
is poition vector of final position minus position vector of initial position )
![begin mathsize 14px style stack A B with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/dd13d277c733f00d7fc32961362628af.png)
Answered by Thiyagarajan K | 05 Aug, 2022, 14:46: PM
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