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## Algebra (all content)

### Unit 19: Lesson 5

Combined vector operations

# Vector operations review

Review the basic vector operations and perform them.

## What are the basic vector operations?

Additionleft parenthesis, a, start subscript, 1, end subscript, comma, b, start subscript, 1, end subscript, right parenthesis, plus, left parenthesis, a, start subscript, 2, end subscript, comma, b, start subscript, 2, end subscript, right parenthesis, equals, left parenthesis, a, start subscript, 1, end subscript, plus, a, start subscript, 2, end subscript, comma, b, start subscript, 1, end subscript, plus, b, start subscript, 2, end subscript, right parenthesis
Subtractionleft parenthesis, a, start subscript, 1, end subscript, comma, b, start subscript, 1, end subscript, right parenthesis, minus, left parenthesis, a, start subscript, 2, end subscript, comma, b, start subscript, 2, end subscript, right parenthesis, equals, left parenthesis, a, start subscript, 1, end subscript, minus, a, start subscript, 2, end subscript, comma, b, start subscript, 1, end subscript, minus, b, start subscript, 2, end subscript, right parenthesis
Scalar multiplicationk, dot, left parenthesis, a, comma, b, right parenthesis, equals, left parenthesis, k, dot, a, comma, k, dot, b, right parenthesis
In vector addition, we add the corresponding components. In vector subtraction, we subtract the corresponding components.
In scalar multiplication, we multiply the scalar by each component.

## Practice set 1: Adding and subtracting vectors

Problem 1.1
u, with, vector, on top, equals, left parenthesis, 1, comma, minus, 5, right parenthesis
w, with, vector, on top, equals, left parenthesis, 8, comma, 4, right parenthesis
u, with, vector, on top, plus, w, with, vector, on top, equals, left parenthesis
,
right parenthesis

Want to try more problems like this? Check out this exercise.

## Practice set 2: Scalar multiplication

Problem 2.1
w, with, vector, on top, equals, left parenthesis, minus, 1, comma, minus, 3, right parenthesis
6, w, with, vector, on top, equals, left parenthesis
,
right parenthesis

Want to try more problems like this? Check out this exercise.

## Practice set 3: Combined operations

Problem 3.1
u, with, vector, on top, equals, left parenthesis, minus, 1, comma, minus, 7, right parenthesis
w, with, vector, on top, equals, left parenthesis, 3, comma, 1, right parenthesis
2, u, with, vector, on top, plus, left parenthesis, minus, 3, right parenthesis, w, with, vector, on top, equals
left parenthesis
,
right parenthesis

Want to try more problems like this? Check out this exercise.