Math Problem Statement
Solution
To find the unit vector in the same direction as v = 2i + 2j - k, we need to normalize this vector. The unit vector is given by the formula:
Where is the magnitude of vector , and it's calculated as:
For , we have:
Now, calculate the magnitude:
Now, divide each component of the vector by the magnitude to get the unit vector:
Thus, the unit vector in the same direction as v is:
Would you like more details, or have any questions on this?
Related Questions:
- What is the formula for finding the unit vector in general?
- How do you calculate the magnitude of a vector in 3D space?
- Can the direction of a vector be changed by normalizing it?
- What are the applications of unit vectors in physics and engineering?
- How do you compute the dot product between two vectors?
Tip: The unit vector is often used to indicate direction without affecting magnitude, making it especially useful in physics problems involving direction or force.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Vector Algebra
Unit Vectors
3D Vectors
Formulas
Unit vector formula: \(\hat{v} = \frac{\vec{v}}{|\vec{v}|}\)
Magnitude formula for 3D vector: \(|\vec{v}| = \sqrt{v_x^2 + v_y^2 + v_z^2}\)
Theorems
-
Suitable Grade Level
Grade 10-12