MATH 105 Lecture Notes - Lecture 10: Scalar Multiplication, Parallelogram, Negative Number
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MATH 105 Lecture 10 Vectors
Difference between a vector and a point
- Vectors are displacements in space
- Which gives them a ‘direction’ and magnitude
- Points are locations in space
- Operations are allowed between points and vectors:
- Subtracting 2 points yields a vector
- Adding a point to a vector gives a point
Vector addition and subtraction
To add or subtract 2 vectors, we add or subtract them with their corresponding components.
E.g.
- The sum of 2 or more vectors is called the resultant
- The resultant of 2 vectors can be found using either the parallelogram method
or triangle method
Parallelogram Method
Addition:
Document Summary
Which gives them a direction" and magnitude. Operations are allowed between points and vectors: Adding a point to a vector gives a point. To add or subtract 2 vectors, we add or subtract them with their corresponding components. The sum of 2 or more vectors is called the resultant. The resultant of 2 vectors can be found using either the parallelogram method or triangle method. Addition: draw the vectors so that their initial points coincide, complete the parallelogram, draw the diagonal and that is the resultant. Subtraction: draw the vectors so that their initial points coincide, complete the parallelogram, draw the diagonal and that is the resultant. A scalar factor is a quantity, sooed, distance or temperature that has size but no direction. Scalar multiplication is simply multiplying the scalar with each component of the vector. Scalar multiplication by a positive number other than 1 changes the magnitude of the vector but not its direction.
