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### Course: 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$\left({a}_{1},{b}_{1}\right)+\left({a}_{2},{b}_{2}\right)=\left({a}_{1}+{a}_{2},{b}_{1}+{b}_{2}\right)$
Subtraction$\left({a}_{1},{b}_{1}\right)-\left({a}_{2},{b}_{2}\right)=\left({a}_{1}-{a}_{2},{b}_{1}-{b}_{2}\right)$
Scalar multiplication$k\cdot \left(a,b\right)=\left(k\cdot a,k\cdot b\right)$
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
$\stackrel{\to }{u}=\left(1,-5\right)$
$\stackrel{\to }{w}=\left(8,4\right)$
$\stackrel{\to }{u}+\stackrel{\to }{w}=\left($
,
$\right)$

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

## Practice set 2: Scalar multiplication

Problem 2.1
$\stackrel{\to }{w}=\left(-1,-3\right)$
$6\stackrel{\to }{w}=\left($
,
$\right)$

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

## Practice set 3: Combined operations

Problem 3.1
$\stackrel{\to }{u}=\left(-1,-7\right)$
$\stackrel{\to }{w}=\left(3,1\right)$
$2\stackrel{\to }{u}+\left(-3\right)\stackrel{\to }{w}=$
$\left($
,
$\right)$

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

## Want to join the conversation?

• is there anything like four dimensional vectors?
• Vectors can exist in any number of dimensions, including infinite dimensions.
• 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?
• 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!
• Are these vectors similar to addition of I cap, Y cap and Z cap
• what does vector a cross vector b mean??
Is it same as vector multiplied by a scalar or dot product??
• Two parallel vectors 'A' & 'B' are added. What will be their resultant?