In this case, vector a and b can make an angle?

Indranil

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In this case, could you tell me please vector a and b in the triangle above can make an angle? please see the image below:
 

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It looks like vectors a and b subtend an angle of 120° and so the angle pointed to in the triangle would be supplementary to that, or 60°.
 
In this case …
Which case are you asking about? There are two different diagrams containing vectors a and b.


… vector a and b in the triangle above can make an angle? …
I don't understand this English.

It's obvious that vectors a and b make angles. You must be trying to ask something else. Please restate your question.

Two of the angles in the triangle are labeled. If you're trying to find the measure of the third angle, that's easy. :cool:

60° + 60° + X° = 180°

Solve for X.
 
Which case are you asking about? There are two different diagrams containing vectors a and b.


I don't understand this English.

It's obvious that vectors a and b make angles. You must be trying to ask something else. Please restate your question.

Two of the angles in the triangle are labeled. If you're trying to find the measure of the third angle, that's easy. :cool:

60° + 60° + X° = 180°

Solve for X.
In the first diagram, can a and b vectors make an angle because two vectors make an angle when either their head to head or tail to tail attached, which you can see in the second diagram where the tail of the vector a and the tail of the vector b attached together?
 
Yes, two vectors form an angle when they are placed head-to-tail, tail-to-head, head-to-head, or tail-to-tail.
 
In the first diagram, can a and b vectors make an angle because two vectors make an angle when either their head to head or tail to tail attached, which you can see in the second diagram where the tail of the vector a and the tail of the vector b attached together?

The real issue is not whether they "make" an angle, but how that angle is related to the vectors. Depending on how the vectors are related and where the angle you are asking about is located, it will be found in different ways. As MarkFL said, for the angle you are asking about, you have to take the supplement. Can you see why?
 
The real issue is not whether they "make" an angle, but how that angle is related to the vectors. Depending on how the vectors are related and where the angle you are asking about is located, it will be found in different ways. As MarkFL said, for the angle you are asking about, you have to take the supplement. Can you see why?
No, could you explain, please?
 
Will you please post the complete exercise, so that we can see what you were given and what you've been asked to do?

I cannot understand what you're trying to talk about, and I cannot read your tiny-print image.
 
No, could you explain, please?

Let's superimpose the two diagrams:

fmh_0002.jpg

Do you see now that \(\displaystyle \theta\) (the angle in question) and \(\displaystyle 120^{\circ}\) are supplementary, that is:

\(\displaystyle \theta+120^{\circ}=180^{\circ}\)

Now, solve for \(\displaystyle \theta\)...what do you get?
 
Let's superimpose the two diagrams:

View attachment 9927

Do you see now that \(\displaystyle \theta\) (the angle in question) and \(\displaystyle 120^{\circ}\) are supplementary, that is:

\(\displaystyle \theta+120^{\circ}=180^{\circ}\)

Now, solve for \(\displaystyle \theta\)...what do you get?
θ = 60° but still I have a question. How did you get 180° by joining two a-vectors by their head to tail? as we know head to head or tail to tail of vectors make an angle
 
Indranil,

Have you taken a formal course in Geometry (at high school or higher level). If not - take that geometry course (face-face, possibly at a community college) first before attempting to solve problems in vector algebra.
 
… How did you get 180° by joining two a-vectors …

The two a vectors in Mark's diagram are joined to form a line.

180° is an angle where the initial ray and terminal ray are on the same line.

Mark superimposed two diagrams. Don't be confused that the terminal ray of the 180° angle points toward the angle's vertex. That's just a consequence of the superposition. The main point he illustrates is that vector b has rotated counterclockwise 120° from the initial ray, and that it has to rotate an additional 60° to form a 180° angle; hence, the angles 120° and the angle (I think) you've been seeking (60°) must be supplementary. Subtracting 120° from 180° is what calculates that 60° angle for you.
 
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