Math Problem Statement
what is teh angle between the vector i + 2j + 3k and the x axis
Solution
To find the angle between the vector and the -axis, we use the dot product formula.
Given:
- Vector
- Unit vector along the -axis is (which can be written as )
The dot product is given by:
The magnitude of is:
The magnitude of is:
Now, the angle between and the -axis is found using the dot product formula:
So, the angle is:
This is the exact value of the angle. To express it as a decimal:
Summary:
The angle between the vector and the -axis is approximately 74.5 degrees.
Would you like more details or have any questions? Here are some related questions to explore:
- What is the angle between the vector and the -axis?
- How would you find the angle between two arbitrary vectors?
- Can the dot product be negative, and what does that signify?
- What are some properties of the dot product of two vectors?
- How would you calculate the projection of one vector onto another?
Tip: When calculating angles between vectors, always ensure both vectors are expressed in the same coordinate system!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Vector Mathematics
Dot Product
Trigonometry
Formulas
Dot Product Formula: v · u = |v| |u| cos(θ)
Magnitude of a Vector: |v| = √(x^2 + y^2 + z^2)
Cosine Inverse: θ = cos^(-1)(x)
Theorems
Dot Product Theorem
Suitable Grade Level
Grades 10-12