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Subtracting Vectors

Key Concept:

  • Vector subtraction involves subtracting corresponding components of two vectors.

  • If x=[x1,x2] and y=[y1,y2], then:

x−y=[x1−y1, x2−y2]
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  • The result is a new vector representing the displacement from y to x

Example: Subtract Vectors x=[2,3] and y=[−4,−2]

1. Given vectors:

  • x=[2,3]
  • y=[−4,−2]

2. Subtraction formula:

x−y = [x1−y1, x2−y2]
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3. Component-wise subtraction:

x−y=[2−(−4),3−(−2)]
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4. Simplify:

x−y=[2+4,3+2]=[6,5]
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5. Result:

 x−y=[6,5]
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Observations:

Subtracting x effectively adds the opposite of y to x.
The result [6,5] represents the displacement vector between
x and y.

subtraction-example

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