# Resultant vector

1. Nov 11, 2014

### gracy

angle between two vectors is 90 degrees ,and they are added by parallelogram method ,what will be the angle between resultant and any of the two vectors?shouldn't it be necessarily 45 degrees in such case which i have mentioned i.e when angle between two vectors is 90 degrees

2. Nov 11, 2014

### UncertaintyAjay

No, it doesn't have to be 45 degrees
When the vectors are perpendicular to each other, the parallelogram will be a rectangle, and the magnitude of the resultant given by phythagoras's theorem. The angle will depend on the magnitudes of the vectors that you are adding. If they are both equal then , yes, the angle will indeed be 45 degrees. Otherwise, the angle will vary. Try it for yourself. Draw two vectors perpendicular to each other ,with different magnitudes , and measure the angle with the resultant. It won't be 45 degrees.

3. Nov 11, 2014

### Vagn

It would depend on the magnitude of the components (i.e. the magnitude of the original two vectors). If the two original vectors had the same magnitude, then they will be at 45 degrees to the resultant, but this is not the case for any arbitrary magnitude.

4. Nov 11, 2014

### gracy

but what happens in case of two vectors which are perpendicular to each other but with different magnitude such as in rectangle ,will the the angle between resultant and other two vectors would be 30-60 so that triangle formed is 30-60-90 or can have any two arbitrary angles which add up to 90 such as 70 &20( because one angle has to be 90)?

5. Nov 11, 2014

### UncertaintyAjay

The angles will be arbitrary. The 30- 60- 90 thing will again be for special cases. Like I said, draw the different cases. See if you can get ones where the angles are, say, 35-55-90, or 70-20-90 and see what magnitudes you'll need( or what ratio of magnitudes, because the angle remains the same if you multiply both by the same factor). Checking these things out for yourself is the best thing to do.Better, even, than asking on PF(- blasphemy)

6. Nov 11, 2014

### gracy

ok i understood.thanks a lot i not only like your answer but also suggestion.so i worked out by myself 30 -60-90 would be another special case when magnitude of one vector is square root 3 times of another vector right?if you don't mind can you answer one more question i already have figured it out but i just want verification ,is resultant more towards the vector which has greater magnitude than which has less magnitude

7. Nov 11, 2014

### UncertaintyAjay

Yeah

8. Nov 11, 2014

### gracy

ok one more question in my homework question i had two add two vectors to x axis .i thought can't i add one vector by parallelogram method and one by triangular law of addition to the x axis at the same time?

9. Nov 11, 2014

### UncertaintyAjay

I'm not entirely sure what you mean by "add vectors to the x axis. The x axis is a reference. You can't add stuff to it. You add components that lie along it, or parallel to it.
Also, whether you use the parallelogram law or the triangle law, you get the same answer. So could you you just clarify your question a wee bit?

10. Nov 11, 2014

### gracy

11. Nov 11, 2014

### Staff: Mentor

You are saying that we have three vectors to add (let's call them A, B, and C) and you want to add them by doing the head-to-tail triangle method for A+B and then the tail-to-tail parallelogram method for A and C? If you do that, you've correctly calculated the two vectors A+B and A+C, but that's not the same as calculating the vector A+B+C which you would get by adding the three vectors.

To add the three vectors, you would calculate the vector V=A+B using either the parellogram or the triangle method, and then calculate your final answer V+C, again using either method, but on V and C this time.

12. Nov 11, 2014

### UncertaintyAjay

Yeah, Nuggatory is right, and btw its a fairly legitimate question

13. Nov 11, 2014

### gracy

thanks.

14. Nov 14, 2014

### gracy

in one numerical of vector involving car and it's path question is as follows .A spy report about a suspected car reads as follows. "The car moved 2.00km towards east, made a perpendicular left turn,ran for 500m, made a perpendicular right Turn, ran for 4.00km and stopped". Find the displacement of the car.I DON'T WANT THIS PROBLEM'S SOLUTION I JUST WANT TO ASK WHAT IS MEANT BY perpendicular left turn & perpendicular right Turn?HOW CAN I DRAW THEM IN FORM OF VECTORS?SIMILARLY IN A NUMERICAL A carrom board (4ft*4ft square) has the queen at the centre. The queen,hit by the striker moves to the front edge and rebounds and goes in the hole behind the striking line.I WANT TO ASK WHAT IS FRONT EDGE IN CARROM?

Last edited: Nov 14, 2014
15. Nov 14, 2014

### UncertaintyAjay

Perpendicular left turn means that the car turns left through 90 degrees.
So if you have a vector represented by an arrow like this
---->
A perpendicular left turn would mean that the new vector representing the cars direction and speed would be pointing up. A perpendicular right would point down.

16. Nov 14, 2014

### gracy

oh you mean if you have a vector represented by an arrow like this → taking perpendicular left turn from here means ↑such that these two arrows make 90 degrees with each other like this.....................................................................................................................................................→

Last edited: Nov 14, 2014
17. Nov 14, 2014

### UncertaintyAjay

Exactly

18. Nov 14, 2014

### gracy

and what about FRONT EDGE IN CARROM?do you have any idea?

19. Nov 14, 2014

### UncertaintyAjay

What's the front edge in carrom?

20. Nov 14, 2014

### sophiecentaur

You can add together as many vectors as you like (and in any order, you like). The tail of the next vector starts at the head of the last one. This is just like instructions to someone walking in a field: "Bearing 000: 25 paces, bearing 030: 10 paces, bearing 150: 60 paces etc. etc". Often the chosen steps are in x and y directions.
The idea of resolving vectors is a clever one and it is usually convenient (but not totally universal) to use right angled (cartesian) axes because they are 'independent' of each other.
Students (that includes me, years ago) often ask WHY choose a particular pair of xy axes. It is arbitrary but there is usually a pair of directions that make the sums easier and you soon get to recognise which directions to choose for best.