How do you find the coordinate of a vector with the unit vector?

In summary, to find the coordinate of a vector with the unit vector, use the formula c = v * u. A unit vector is a vector with a magnitude of 1 and is important in vector calculations. To determine the unit vector of a given vector, find the magnitude and divide each component by it or use the formula u = v / ||v||. Unit vectors are important in vector calculations as they simplify calculations and represent vectors in different coordinate systems. Unit vectors cannot be negative, as they must have a magnitude of 1 and represent a specific direction.
  • #1
BlueRope
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If you already have one of the two coordinates?
 
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  • #2
If ##x=x_1e_1+x_2e_2## and you know the value of ##x_1##, you can get the value of ##x_2## from ##x_2e_2=x-x_1e_1##.

Another option (if you understand inner products) is to just compute ##\langle e_2,x\rangle##.
 

1. How do you find the coordinate of a vector with the unit vector?

To find the coordinate of a vector with the unit vector, you can use the formula c = v * u, where c is the coordinate, v is the vector, and u is the unit vector. This formula calculates the magnitude of the vector in the direction of the unit vector.

2. What is a unit vector?

A unit vector is a vector that has a magnitude of 1 and is used to represent a specific direction in a coordinate system. It is commonly denoted by the symbol u and is important in vector calculations and geometry.

3. How do you determine the unit vector of a given vector?

To determine the unit vector of a given vector, you must first find the magnitude of the vector. Then, divide each component of the vector by the magnitude to get the unit vector. Alternatively, you can use the formula u = v / ||v|| where u is the unit vector and v is the given vector.

4. Why are unit vectors important in vector calculations?

Unit vectors are important in vector calculations because they help us understand the direction and magnitude of a vector. They also simplify calculations and make it easier to represent vectors in different coordinate systems.

5. Can you have a negative unit vector?

No, unit vectors cannot be negative. They must have a magnitude of 1 and can only represent a specific direction in a coordinate system. If a vector has a negative direction, it can be represented by multiplying it with a negative scalar value, but the resulting unit vector will still have a magnitude of 1.

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