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] 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] 3. Component-wise subtraction: x−y=[2−(−4),3−(−2)] 4. Simplify: x−y=[2+4,3+2]=[6,5] 5. Result: x−y=[6,5] Observations: Subtracting x effectively adds the opposite of y to x. The result [6,5] represents the displacement vector between x and y.
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]
- 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]
3. Component-wise subtraction:
x−y=[2−(−4),3−(−2)]
4. Simplify:
x−y=[2+4,3+2]=[6,5]
5. Result:
x−y=[6,5]
Observations:
Subtracting x effectively adds the opposite of y to x.
The result [6,5] represents the displacement vector between
x and y.
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