Math Problem Statement
Let Bold u equals negative 7 Bold i plus 8 Bold j , Bold v equals 8 Bold i minus Bold j , and Bold w equals negative 2 Bold i . Find 4 Bold u minus left parenthesis 3 Bold v minus Bold w right parenthesis . Question content area bottom Part 1 4 Bold u minus left parenthesis 3 Bold v minus Bold w right parenthesis
=
Solution
We are given the following vectors:
We need to compute:
Step 1: Compute
Multiply each component of vector by 4:
Step 2: Compute
Multiply each component of vector by 3:
Step 3: Compute
Now subtract vector from :
Simplifying:
Step 4: Compute
Now subtract from :
Distribute the subtraction:
Simplifying:
Final Answer:
Would you like to see more details or explore any specific steps? Here are a few related questions:
- How would you compute a similar expression involving 5 vectors?
- What is the geometric interpretation of subtracting vectors?
- How do you find the magnitude of a vector resulting from an operation like this?
- How do you apply vector operations to solve real-world problems?
- How would you extend this to 3-dimensional vectors?
Tip: When performing vector operations, always break each vector into its components and deal with them separately.
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Math Problem Analysis
Mathematical Concepts
Vector Operations
Vector Addition and Subtraction
Scalar Multiplication
Formulas
Scalar Multiplication: c * (ai + bj) = (c * a)i + (c * b)j
Vector Addition/Subtraction: (ai + bj) ± (ci + dj) = (a ± c)i + (b ± d)j
Theorems
Vector Addition is Commutative and Associative
Suitable Grade Level
Grades 10-12