Question

How do I solve this equation?

Answer 1

General Formulas and Concepts

Pre-Calculus

Vectors

Vector Properties:

• Addition:
  
  `\displaystyle < a, b > + < c, d > = < a + c, b + d >`
• Subtraction:
  
  `\displaystyle < a, b > - < c, d > = < a - c, b - d >`

Application

Step 1: Define

Let's organize what the problem gives us:

• We are given a vector
  `\displaystyle \vec{s} = < -2, 9 >`
• We are given another vector
  `\displaystyle \vec{t} = < -1, 1 >`
• We are asked to find the sum
  `\displaystyle \vec{s} + \vec{t}`

Step 2: Work

In order to add vectors, we simply combine each of the respective components from both vectors. This can be visualized via Vector Properties above. We apply that concept in this problem:

`\displaystyle\begin{aligned}\vec{s} + \vec{t} & = < -2 + -1, 9 + 1 > \\& = \boxed{ < -3, 10 > }\end{aligned}`

Answer

`\displaystyle \therefore \boxed{ \vec{s} + \vec{t} = < -3, 10 > }`

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Topic: Pre-Calculus

Unit: Vectors