Math Problem Statement
Solution
The task is asking for the determination of the norm (or magnitude) of a vector , given its components in a coordinate system.
From the image, we see the vector , and we are working in an orthonormal reference frame, meaning the vectors and are orthogonal and of unit length.
To find the norm of vector , we use the formula for the norm of a 2D vector:
Let's compute this:
Thus, the norm of vector is .
Would you like more details on how this formula is derived, or do you have any questions? Here are a few related questions that might help expand on this concept:
- How is the norm of a vector used in various applications?
- How do you compute the norm of a 3D vector?
- What is the relationship between the direction of a vector and its norm?
- Can the norm of a vector be negative?
- How do you find the unit vector corresponding to a given vector?
Tip: Always check that you're using the correct component values (i.e., and coordinates) when applying the formula for vector magnitude.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Vector Norm
Coordinate Systems
Orthogonal Vectors
Formulas
|u| = √(x^2 + y^2)
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 9-11