CBSE Class 11-science Answered
if |A|=|B|=|A-B|, then find the angle b/w the two vectors
Asked by kaziryan.05 | 13 Apr, 2022, 21:01: PM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/5369bf28ba652f562ecd5244e76c2b8a6256f1465f53d0.42508574fa.png)
Let
=
and
=
. Let θ be the angle between the vectors
and
.
![begin mathsize 14px style stack O P with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/19a9728774b667349a0a39e761916f4e.png)
![begin mathsize 14px style A with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/639c73046741125cfeb2fc30eff22313.png)
![begin mathsize 14px style stack O Q with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/59e4f177d93f4ece70bcb44fa31224ca.png)
![begin mathsize 14px style B with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/9543f24d51b195c4f40909021855c5c9.png)
![begin mathsize 14px style A with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/639c73046741125cfeb2fc30eff22313.png)
![begin mathsize 14px style B with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/9543f24d51b195c4f40909021855c5c9.png)
We can construct
= (
-
) as shown in figure.
![begin mathsize 14px style stack O S with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/5a3a583a343d739b176d056993a3b993.png)
![begin mathsize 14px style A with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/639c73046741125cfeb2fc30eff22313.png)
![begin mathsize 14px style B with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/9543f24d51b195c4f40909021855c5c9.png)
OSPQ is parallelogram and PQ = | (
-
) |
![begin mathsize 14px style A with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/639c73046741125cfeb2fc30eff22313.png)
![begin mathsize 14px style B with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/9543f24d51b195c4f40909021855c5c9.png)
As per the given condition , |
| = |
| = | (
-
) | , all the sides of ΔOPQ are same .
![begin mathsize 14px style A with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/639c73046741125cfeb2fc30eff22313.png)
![begin mathsize 14px style B with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/9543f24d51b195c4f40909021855c5c9.png)
![begin mathsize 14px style A with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/639c73046741125cfeb2fc30eff22313.png)
![begin mathsize 14px style B with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/9543f24d51b195c4f40909021855c5c9.png)
Hence θ = 60o = ( π / 3 ) rad
Hence angle between
and
is 60o or ( π / 3 ) rad
![begin mathsize 14px style A with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/639c73046741125cfeb2fc30eff22313.png)
![begin mathsize 14px style B with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/9543f24d51b195c4f40909021855c5c9.png)
Answered by Thiyagarajan K | 13 Apr, 2022, 21:39: PM
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