Value of an unusual vector notation

[Raghav Gupta]

Homework Statement

If a,b,c are three -zero vectors such that each one of them are perpendicular to the sum of the other two vectors, then the value of | a, b, c|² is
|a|² + |b|² + |c|²
|a| + |b| + |c|
2(|a|² + |b|² + |c|²)
½(|a|² + |b|² + |c|²)

Homework Equations

a.b = ab cosθ
|axb|= ab sinθ

The Attempt at a Solution

First I am not understanding the notation in question of which we have to find value.
It does not makes sense of having three zero vectors.

 

[ehild]

Homework Statement

If a,b,c are three -zero vectors...

The Attempt at a Solution

First I am not understanding the notation in question of which we have to find value.
It does not makes sense of having three zero vectors.

Either it is a typo or you misread something. It should be

If a,b,c are three non-zero vectors...

 

[Raghav Gupta]

Either it is a typo or you misread something. It should be

If a,b,c are three non-zero vectors...

No, I have not made typo or misread.
Maybe the question has misprint, what if they are non zero?

 

[Raghav Gupta]

I think the question is saying that
If a,b, c are three-zero( 3-0= 3 ) vectors, .

 

[ehild]

No, I have not made typo or misread.
Maybe the question has misprint, what if they are non zero?

Then the question has a misprint. It is a very usual condition in problems about vectors. "Three-zero vectors" has no sense. Three non-zero vectors has. Neither of a,b,c are nullvector. If one of them was zero vector, how could it be perpendicular to the sum of the other two?

 

[Raghav Gupta]

Then the question has a misprint. It is a very usual condition in problems about vectors. "Three-zero vectors" has no sense. Three non-zero vectors has. Neither of a,b,c are nullvector. If one of them was zero vector, how could it be perpendicular to the sum of the other two?

Okay, what if they are non- zero, how to solve then?

 

[ehild]

Okay, what if they are non- zero, how to solve then?

That is your problem. What does it mean that every vector is perpendicular to the sum of the other two? You can get a condition for the sum of the products...

 

[Raghav Gupta]

That is your problem. What does it mean that every vector is perpendicular to the sum of the other two? You can get a condition for the sum of the products...

But what |a,b,c| means
Shouldn't the question be[a b c ] ?

 

[ehild]

I do not know the notations your books use . Look after in the book or notes where you got the problem from.

 

[Raghav Gupta]

I do not know the notations your books use . Look after in the book or notes where you got the problem from.

That question was asked in test and I am asking that because I myself am not sure of notation.
Haven't you seen my attempt in template, because you are asking those questions which I am asking.

Maths notations are same worldwide and do you not know Maths is a universal language?
Is that a misprint also |a,b,c | and should it have been |a.b.c| or [ a b c ]
[a b c ] is scalar triple product also written as a. (b x c) ?

 

[ehild]

Was it in a test given to you? If yes, you should ask your teacher what he/she meant.
Math notations are not the same everywhere. I saw quite many different notations for functions, vectors, derivatives, partial derivatives.. Even in the same college, different teachers use completely different notations.
A Maths book usually starts with a page about the notations.
|a, b, c| can be the magnitude of the scalar triple product $\vec a \cdot (\vec b \times \vec c)$ .
But I think most probable, that the problem was copied several times, and has changed, and the original one sounded as

If a,b,c are three non-zero vectors such that each one of them are perpendicular to the sum of the other two vectors, then the value of | a + b + c|² is
|a|² + |b|² + |c|²
|a| + |b| + |c|
2(|a|² + |b|² + |c|²)
½(|a|² + |b|² + |c|²).

Why do I think so?

If it was the magnitude of the scalar triple product, it would be the volume of a parallelepiped with dimension length³. All but one (which is linear) the given answers are of dimension length².

| a + b + c|² is a nice problem and rather easy to solve. Try . And do not worry about a badly-worded problem.

 

[Raghav Gupta]

Yeah, then it is easy to solve,
(a+b+c).(a+b+c) = a.a + b.b + c.c other terms are zero .
|a+b+c|²= |a|² +|b|² +|c|².
Thanks ehild for the intuition. The problem was badly stated.

 

[ehild]

Yeah, then it is easy to solve,
(a+b+c).(a+b+c) = a.a + b.b + c.c other terms are zero .

Are you sure? How did you get it?

|a+b+c|²= |a|² +|b|² +|c|².
Thanks ehild for the intuition. The problem was badly stated.

Somebody typing those problems does his work bad.

 

[Raghav Gupta]

Are you sure? How did you get it?

Somebody typing those problems does it bad.

Yeah I am sure,
(a+b+c).(a+b+c)= a.a + b.b + c.c + a.(b+c) + b.(a+c) + c.(a+b)
Now the bold parts are zero as it is given one vector is perpendicular to the sum of other vectors.
Is that correct.

Why were you asking for sureness?

 

[ehild]

Yeah I am sure,
(a+b+c).(a+b+c)= a.a + b.b + c.c + a.(b+c) + b.(a+c) + c.(a+b)
Now the bold parts are zero as it is given one vector is perpendicular to the sum of other vectors.
Is that correct.

Why were you asking for sureness?

I just wanted to know, and I wanted you to show the whole work. It is useful to those who read the thread and want to learn from it,