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Questions and Answers
When adding two vectors using the head-to-tail rule, where is the resultant vector drawn from?
When adding two vectors using the head-to-tail rule, where is the resultant vector drawn from?
- The head of the first vector to the head of the second vector
- The tail of the first vector to the head of the second vector (correct)
- The tail of the first vector to the tail of the second vector
- The head of the first vector to the tail of the second vector
What is the property of vector addition that allows vectors to be added in any order?
What is the property of vector addition that allows vectors to be added in any order?
- Associative
- Distributive
- Commutative (correct)
- Scalar Multiplication
What is subtracting a vector equivalent to?
What is subtracting a vector equivalent to?
- Adding the negative of the vector (correct)
- Dividing the vector by -1
- Multiplying the vector by -1
- Adding the same vector
What is the geometrical method of subtracting vector b from vector a?
What is the geometrical method of subtracting vector b from vector a?
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What is a property of vector subtraction?
What is a property of vector subtraction?
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Study Notes
Vector Addition
- Head-to-Tail Rule: To add two vectors, place the tail of the second vector at the head of the first vector.
- The resultant vector is drawn from the tail of the first vector to the head of the second vector.
- Properties:
- Commutative: The order of vectors does not change the result.
- Associative: Vectors can be added in any order.
Vector Subtraction
- Equivalent to Adding the Negative: Subtracting a vector is equivalent to adding its negative.
- To subtract vector b from vector a, add -b to a.
- Geometrically: Place the tail of -b at the head of a, then draw the resultant vector from the tail of a to the head of -b.
- Properties:
- Not commutative: The order of vectors matters.
- Not associative: Vectors must be subtracted in a specific order.
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Description
Learn about the head-to-tail rule, properties, and geometric representation of vector addition and subtraction. Understand how to add and subtract vectors, and the rules that govern these operations.
