Calculating |vect.A + Vect.B + Vect.C|

  • Thread starter draotic
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In summary, if three mutually perpendicular unit vectors A, B, and C are given, the magnitude of their sum is equal to the square root of 3.
  • #1
draotic
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Homework Statement


vector A,B and C are mutually perpendicular unit vectors , then |vect.A + Vect.B + Vect.C| is equal to ...?


Homework Equations


unit vector=vector/magnitude


The Attempt at a Solution


since they are unit vectors and are perpendicular..they obviously are lying along x , y and z axes denoted by i , j , k (caps)
 
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  • #2
Are we sure that this is a 3 dimensional incident?

Edit: I just realized, I clicked on "Advanced Physics" . . . going to go back to the Introductory forum now.

Good luck :).
 
  • #3
Three unit vectors can be mutually perpendicular, but it is not necessary for the three vectors to coincide, or lie along, the coordinate axes.

Remember, if two arbitrary vectors A and B are defined such that A dot B = 0, then A and B are perpendicular. If we form the cross product such that C = A cross B, then the vectors A, B, and C will be mutually perpendicular.

The magnitude is given by the standard Euclidean norm Sqrt(A^2 + B^2 + C^2).
 

FAQ: Calculating |vect.A + Vect.B + Vect.C|

How do you calculate the magnitude of a vector sum?

To calculate the magnitude of a vector sum, you will need to find the sum of the squares of the vector's components. Then, take the square root of the sum to find the magnitude.

What is the formula for calculating |vect.A + Vect.B + Vect.C|?

The formula for calculating the magnitude of a vector sum is |vect.A + Vect.B + Vect.C| = √(Ax + Bx + Cx)^2 + (Ay + By + Cy)^2 + (Az + Bz + Cz)^2

Can the magnitude of a vector sum be negative?

No, the magnitude of a vector sum cannot be negative. It is always a positive value, representing the distance or length of the vector.

What are the units for the magnitude of a vector sum?

The units for the magnitude of a vector sum will depend on the units of the vector's components. For example, if the components are in meters, the magnitude will be in meters.

Are there any special cases when calculating the magnitude of a vector sum?

Yes, there are special cases when calculating the magnitude of a vector sum. For instance, if one or more of the vector's components is zero, the magnitude will also be zero. Additionally, if the vectors are perpendicular to each other, the magnitude can be calculated using the Pythagorean theorem.

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