Writing the vector with a given magnitude in the direction of another vector

The video tutorial explains how to find a vector V with a magnitude of 9 in the same direction as vector W, which is 7i + 3j. The instructor demonstrates that vector W does not have a magnitude of 9 and shows how to convert it into a unit vector. By dividing vector W by its magnitude, a unit vector is obtained. This unit vector is then multiplied by 9 to achieve the desired vector V with a magnitude of 9. The tutorial emphasizes the importance of unit vectors in maintaining direction while changing magnitude.

What is the magnitude of the vector W described in the text?

What is the significance of the Pythagorean theorem in determining the magnitude of vector W?

How can you determine if a vector has a magnitude of nine?

What is a unit vector and why is it important in this context?

Describe the process of converting a vector to a unit vector.

What is the final form of the vector V that has a magnitude of nine?

Explain how to find a new vector with a different magnitude while maintaining the same direction.