Tricky Angles

Geometry Level 3

Find the angle (in degrees) between the vectors shown in the diagram?

60 210 150 -30 30

2 solutions

Rohit Gupta
May 31, 2015

Angle between the vectors has to lie between 0-180 degrees. The angle between the vectors is measured when they are connected either tail to tail or head to head. In the question given the vectors are connected tail to head and therefore 210 or 360-210 degrees is not the right option to give.
So first move one of the vectors such that they are connected tail to tail and then see the smaller angle between the two which will be 210-180 degrees = 30 degrees.

$\bullet$ Is it just convention or it has some reason that angle is measured when they are connected either tail to tail or head to head. ?

$\bullet$ And If I say that the angle between two given vectors is $280^\circ$ , then does it imply that the angle between them is $80^\circ$ .

Sandeep Bhardwaj - 6 years ago

Oh, I really want Rohit Sir to answer your question! @Sandeep Bhardwaj @Rohit Gupta Rohit Sir, He's one of your most succesful students!

Swapnil Das - 6 years ago

hahahaha..May be You're right. :P But I too want the answer from Rohit Sir's end.

Sandeep Bhardwaj - 6 years ago

@Sandeep Bhardwaj – Here I would simply say Vectors is a part of Mathematics..!! :P
The angle we need to choose while using vector laws of addition can be calculated by connecting the vectors tail to tail or head to head and counting the smaller angle between them, you me choose to find this angle by other ways as well but you will end up with the same answer. According to me its not right to say the angle between the two vectors is 280 degree..We should mention the angle as 80 degree only.

The reason behind joining the vectors tail to tail and head to head is that we have free vectors to deal with in physics and they can be shifted parallel to themselves if you do not attach a rule to find the angle everyone will report a different angle!!

Rohit Gupta - 6 years ago

Here the angle is in anticlockwise sense..must it not be -ve....

Vishal Subedi - 5 years, 8 months ago

Azadali Jivani
Aug 13, 2015

210 - 180 = 30 (Ans.)

Tricky Angles

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