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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?

Addition | left 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 | |

Subtraction | left 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 multiplication | k, 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.

*Want to learn more about vector addition and subtraction? Check out this video.*

In scalar multiplication, we multiply the scalar by each component.

*Want to learn more about scalar multiplication? Check out this video.*

## Practice set 1: Adding and subtracting vectors

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

## Want to join the conversation?

- is there anything like four dimensional vectors?(18 votes)
- Vectors can exist in any number of dimensions, including infinite dimensions.(28 votes)

- I think the vector operation in algebra is much simpler than the graph.And also if mathematicians go into higher dimensions the vector operation in algebra is much useful than graphing the vector,is it?(12 votes)
- Yes, it is. You can solve a 5-dimensional vector sum quite easily. For example, Vector A (1,2,3,4,5) + Vector B (5,4,3,2,1) = (6,6,6,6,6) [ILLUMINATI!]. But can you imagine a graph with 5 axes? Guess not. Happy learning!(26 votes)

- what does vector a cross vector b mean??

Is it same as vector multiplied by a scalar or dot product??(5 votes)- No. This is called the "cross product" or "vector product". Where the result of a dot product is a number, the result of a cross product is a vector. The result vector is perpendicular to both the other vectors. This means that if you have 2 vectors in the XY plane, then their cross product will be a vector on the Z axis in 3 dimensional space.

The cross product is introduced in this video: https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/linear-algebra-cross-product-introduction(5 votes)

- Is it possible to perform multiplication or division on two vectors?(3 votes)
- There are at least two types of multiplication on two vectors: dot product and cross product. The dot product of two vectors is a number (or scalar), and the cross product of two vectors is a vector. Dot products and cross products occur in calculus, especially in multivariate calculus. They also occur frequently in physics.

Have a blessed, wonderful day!(6 votes)

- Are these vectors similar to addition of I cap, Y cap and Z cap(4 votes)
- In some ways yes they are. If you have further questions, look at this link:

https://math.stackexchange.com/questions/125610/prove-that-x-cap-y-z-x-cap-y-x-cap-z(3 votes)

- Two parallel vectors 'A' & 'B' are added. What will be their resultant?(2 votes)
- That depends, if both are pointing in the same way then direction angle will be the same but the magnitude will be the sum of the two magnitudes. f both are pointing in opposite directions then direction angle will be the same as the larger on and the magnitude will be the difference of the two magnitudes.(5 votes)