Math Problem Statement
Solution
The problem given involves vectors and with the following properties:
We need to find the magnitude .
Let's solve this step by step.
Step 1: Use the Magnitude Condition
From the first condition:
Step 2: Use the Second Condition
Squaring both sides: Since , we have : Rearranging:
Step 3: Use the Perpendicular Condition
Since is perpendicular to :
Step 4: Solve the System of Equations
We have the following two equations:
Substitute for in the first equation:
Now, substitute into the second equation:
Therefore, the correct answer is:
So, the correct option is B.
Do you want more details or have any questions?
Here are 5 more questions you might want to ask:
- How do you determine if two vectors are perpendicular?
- Can you explain the dot product in more detail?
- What are some common vector operations and their properties?
- How do you find the magnitude of a vector given its components?
- What are some real-world applications of vector mathematics?
Tip: Always break down complex vector problems into smaller parts and use fundamental vector properties to simplify the solution process.
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Math Problem Analysis
Mathematical Concepts
Vectors
Magnitude of Vectors
Dot Product
Vector Perpendicularity
Formulas
Magnitude of a vector formula
Dot product formula
Theorems
Properties of vector magnitudes
Vector perpendicularity theorem
Suitable Grade Level
Advanced High School
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