I have two vectors: $A = i-3j+2k$ and $B = -3i+4j-k.$

I have already found the angle between the two to be ~$157.6$ degrees, but I am required to find the smallest angle between the two - I am not sure what that means exactly and can't seem to find the answer online. I would be glad if you could help me out with that.


1 Answer 1


They are position vectors in $\mathbb{R}^3$. Two vectors describe a plane so I presume you are being asked to find the angle between the two vectors in the plane they describe.

I've added a small illustration (done in Geogebra) to show what I mean. The two points $A$ and $B$ are described by the vectors you gave. The blue plane is described by $A, B$ and the origin and the angle between these two vectors is $153^{\circ}$ (not sure if the angle is properly visible). You can compute this angle via the dot product. If you used the dot product and got to $157.6^{\circ}$ there may be a rounding error of some description in your calculation. Either way, I believe this may be what your teacher is looking for. Does this help?


  • 2
    $\begingroup$ This would be more appropriate in the comments section. $\endgroup$ Mar 15, 2016 at 20:22
  • $\begingroup$ I agree! My lack of reputation means that I am not yet allowed to comment everywhere. $\endgroup$ Mar 15, 2016 at 20:23
  • $\begingroup$ I am sorry, I did not remember that rule applies. For what it's worth, it's a usefull hint! $\endgroup$ Mar 15, 2016 at 20:25
  • 1
    $\begingroup$ Thanks, I hope it helps the asker. Only 6 more reputation to go before I am deemed trustworthy enough to contribute to the community in the form of comments! Haha $\endgroup$ Mar 15, 2016 at 20:26
  • 1
    $\begingroup$ It's from my teacher's presentation. The answer is not indicated, sadly. $\endgroup$
    – xen20
    Mar 15, 2016 at 20:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.