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Course: Algebra (all content) > Unit 19

Lesson 5: Combined vector operations
Math
Algebra (all content)
Vectors
Combined vector operations
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Vector operations review

Google Classroom
Review the basic vector operations and perform them.

What are the basic vector operations?

Addition(a1,b1)+(a2,b2)=(a1+a2,b1+b2)
Subtraction(a1,b1)−(a2,b2)=(a1−a2,b1−b2)
Scalar multiplicationk⋅(a,b)=(k⋅a,k⋅b)
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

Problem 1.1
u→=(1,−5)
w→=(8,4)
u→+w→=(
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
,
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
)

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

Practice set 2: Scalar multiplication

Problem 2.1
w→=(−1,−3)
6w→=(
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
,
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
)

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

Practice set 3: Combined operations

Problem 3.1
u→=(−1,−7)
w→=(3,1)
2u→+(−3)w→=
(
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
,
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
)

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

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