Cal III/ Multi-V (vector notation troubles)

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In summary, the question asks for the magnitude of the vector ||3A-B||, which can be found by taking the square root of the sum of all its components squared. In this case, the magnitude is 6.
  • #1
The_Chromer
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Homework Statement


Given vector A = i + j - k and vector B= i - j + k, calculate ||3A-B||.

My work can be found here (I am not literate in Latex markups):
http://img714.imageshack.us/img714/732/sixhomeworkproblems001.jpg

I am unfamiliar with the notation of the double bars surrounding this vector combination. I think, and I say that very loosely, that it means to find the normal vector to the plane. If I could get some clarification for that, then I don't think the problem should be too difficult.

Homework Equations


Uncertain of problem notation.

The Attempt at a Solution


http://img823.imageshack.us/img823/8554/attempt001.jpg
 
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  • #2
You're really close. All you have to do is find the magnitude of that vector. The equation for that is the square root of the sum of all of its components squared.
Sqrt(a^2+b^2+c^2).
 
  • #3
Wow. So all the question asks for is the magnitude?

[tex]sqrt(36)[/tex]=6
 

1. What is the concept of vector notation in Cal III/Multi-V?

Vector notation is a mathematical representation of a vector using symbols such as boldface letters, arrows, or parentheses. It is used in Cal III/Multi-V to describe the magnitude and direction of a vector in a 3-dimensional space.

2. How is vector addition and subtraction performed using vector notation in Cal III/Multi-V?

In vector notation, vector addition and subtraction are performed by adding or subtracting the corresponding components of the vectors. For example, if we have vectors A = (a1, a2, a3) and B = (b1, b2, b3), their sum A + B would be (a1 + b1, a2 + b2, a3 + b3).

3. What is the role of unit vectors in vector notation in Cal III/Multi-V?

Unit vectors are vectors with a magnitude of 1 and are used to describe the direction of a vector in a 3-dimensional space. They are denoted by the symbols i, j, and k and are used to express any vector as the sum of its components multiplied by the corresponding unit vectors.

4. How do we represent a vector in both magnitude and direction using vector notation in Cal III/Multi-V?

A vector can be represented in both magnitude and direction using vector notation by using the magnitude of the vector as a coefficient and the unit vector in the direction of the vector as the variable. For example, the vector A = (3, 4, 5) can be represented as A = 3i + 4j + 5k.

5. What is the difference between a scalar and a vector in Cal III/Multi-V?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. Scalars can be represented by a single number, while vectors require multiple components. In Cal III/Multi-V, scalars are used to represent quantities such as temperature or time, while vectors are used to represent quantities such as displacement or force.

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