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Vector Addition and Subtraction

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Questions and Answers

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?

Associative

Distributive

Commutative (correct)

Scalar Multiplication

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?

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 Signup and view all the answers

What is a property of vector subtraction?

The order of vectors matters Signup and view all the answers

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.