Vector Problem: Find Expression for C in Terms of A,B,d

  • Thread starter fahd
  • Start date
  • Tags
    Vector
In summary, the conversation discusses finding an expression for vector C in terms of vectors A and B, and a scalar d, given that A.C=d and A X C = B. The suggested approach is to use component representations of each vector and solve for the components of C using a system of equations. After some trial and error, the final expression is found to be C = (B X A + dA)/|A|^2.
  • #1
fahd
40
0
Vector question-please help

hello.please help me with this vector problem..


Given two vectors A and B and a scalar 'd', it is known that:
A.C=d and A X C = B
where C is a vector of unknown direction and magnitude.Find an expression for C in terms of A,B,d and the magnitude of vector A.

I tried using langranges identity but am getting a value of c's magnitude and not C as a vector..Like I am getting sumthing like
c^2=(B^2+d^2)/B^2 which i know is kinda wrong as the answer iv got is a magnitude and not a vector..
What do i do?Please help! o:)
 
Last edited:
Physics news on Phys.org
  • #2
I'd go with component representations of each vector ([itex]\vec{A}=A_x\hat{i}+A_y\hat{j}+A_z\hat{k}[/itex], etc.) Now if you write out [itex]\vec{A}\times\vec{C}=\vec{B}[/itex] you'll get a 3x3 system of equations for the components of [itex]\vec{C}[/itex]. It will look tempting to solve the system, but you won't be able to (the coefficient matrix is singular). But you could use 2 of those equations, and for the third equation use [itex]\vec{A}\cdot\vec{C}=d[/itex]. Then you should be able to solve for the components of [itex]\vec{C}[/itex]. Once you have those, you're done.
 
Last edited:
  • #3
Tom Mattson said:
I'd go with component representations of each vector ([itex]\vec{A}=A_x\hat{i}+A_y\hat{j}+A_z\hat{k}[/itex], etc.) Now if you write out [itex]\vec{A}\times\vec{C}=\vec{B}[/itex] you'll get a 3x3 system of equations for the components of [itex]\vec{C}[/itex]. It will look tempting to solve the system, but you won't be able to (the coefficient matrix is singular). But you could use 2 of those equations, and for the third equation use [itex]\vec{A}\cdot\vec{C}=d[/itex]. Then you should be able to solve for the components of [itex]\vec{C}[/itex]. Once you have those, you're done.


hi..i tried doing the question and have got an unusual answer..shown on the included attachment..The question said that the answer shud be in terms of A,B,d and magnitude of A.However mine isn't coming as shown..Plz help!Thanks!
 

Attachments

  • scan0002.jpg
    scan0002.jpg
    25.4 KB · Views: 354
Last edited:
  • #4
I think you're going to have to flex your algebra muscles a little more. I really don't feel like solving the whole thing :redface: , but for [itex]C_x[/itex] I get:

[tex]C_x=\frac{da_x-a_yb_z+a_zb_y}{a_x^2+a_y^2+a_z^2}[/tex]
[tex]C_x=\frac{da_x-(\vec{A}\times\vec{B})_x}{|\vec{A}|^2}[/tex].

If the other components go by that pattern, and if I haven't made any dumb mistakes, then it should follow that:

[tex]\vec{C}=\frac{d\vec{A}-\vec{A}\times\vec{B}}{|\vec{A}|^2}[/tex].

Try to work it out, OK?
 
  • #5
A.C=D
AxC=B
So we have
[tex](AXC)XA=|A|^2 C-(C.A)A=BXA[/tex]

So
[tex]C=\frac{BXA+dA}{|A|^2}[/tex]
 
  • #6
heey..i tried working it now and got it...u knw what..the only thing was that everything seemed so abstract that it was confusing me like nething..i mean unknown components etc..
nehow..thanks again..
i finally got it!
 

1. What is a vector problem?

A vector problem involves finding the solution to a mathematical expression involving vectors. Vectors have both magnitude and direction, and are commonly used in physics and engineering.

2. How do you find the expression for C in terms of A, B, and d?

To find the expression for C, you would first need to have a clear understanding of the problem and the given information. Then, you would use vector operations such as addition, subtraction, and scalar multiplication to manipulate the given vectors A, B, and d until you are left with an expression for C.

3. What is the significance of expressing C in terms of A, B, and d?

Expressing C in terms of A, B, and d allows us to better understand the relationship between the given vectors and the unknown vector C. This expression can also be used to solve for the magnitude and direction of C, as well as to make predictions or calculations in future problems.

4. Can you provide an example of a vector problem where C is expressed in terms of A, B, and d?

Sure, for example, let A = <2, 3> and B = <-1, 5> be two given vectors. We want to find the vector C such that C + B = A + d. By rearranging the equation, we get C = A + d - B. Therefore, the expression for C in terms of A, B, and d is C = A + d - B.

5. Are there any tips for solving vector problems and finding the expression for C?

Some tips for solving vector problems and finding the expression for C include drawing a diagram to visualize the problem, using the properties of vectors such as the commutative and distributive properties, and breaking down the problem into smaller, more manageable steps.

Similar threads

  • Introductory Physics Homework Help
Replies
14
Views
232
  • Introductory Physics Homework Help
Replies
3
Views
365
  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
983
  • Introductory Physics Homework Help
Replies
2
Views
2K
Replies
1
Views
467
  • Introductory Physics Homework Help
Replies
14
Views
522
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
13
Views
521
  • Introductory Physics Homework Help
Replies
13
Views
448
Back
Top