# Resultant vector physics problem

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

## Answers and Replies

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.

• 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
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.

• gracy
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.
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)?

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)

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:)eek:- blasphemy)
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

Yeah

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?

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?

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?
i understand why you are not getting my question i just want to ask in triangular law of addition we add one vector to another from head but in parallelogram law tail of both vectors meet at a same point.i know we can either use parallelogram law or the triangle law, but i am asking can't we use both when we have to add two vectors( at different angles)to one single vector such that from that single vector's head one vector is added by triangular law of addition and from that single vector tail another vector is added by parallelogram method in this way we added two vector in one single vector.I REALLY DON'T THINK IT IS RIGHT.SO SORRY IF YOU FIND THIS QUESTION DUMB.BUT I AM HAVING THIS DOUBT AND I BELIEVE IN CLEARING DOUBTS ON THE SPOT .

Nugatory
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.

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

Yeah, Nuggatory is right, and btw its a fairly legitimate question
thanks for all your answers.
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.
thanks.

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

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.

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:
Exactly

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

What's the front edge in carrom?

sophiecentaur
Science Advisor
Gold Member
2020 Award

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.....................................................................................................................................................→
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.

What's the front edge in carrom?
is range (in projectile motion) vector?i mean whether it denotes distance or displacement?if the later then range should be vector, right?

You're right displacement is a vector quantity, but range denotes distance and is a scalar quantity.

sophiecentaur
Science Advisor
Gold Member
2020 Award
You're right displacement is a vector quantity, but range denotes distance and is a scalar quantity.
For the simplest situations you can draw a (range) circle round your starting point to say where you could en up but any influence like wind (definitely a vector) would modify that and affect the final arrival point. It would be unusual for the range to be the only relevant factor in any ballistics problem - you wouldn't want to be sending ordinance behind your own lines haha.

You're right displacement is a vector quantity, but range denotes distance and is a scalar quantity.
thanks.

Np