Writing the component form of a vector given the magnitude and direction vector

The video tutorial explains how to find a new vector with a specified magnitude while maintaining the same direction as a given vector. It covers the calculation of the unit vector and how to scale it to achieve the desired magnitude. The process involves using the formula for magnitude and applying scalar multiplication to obtain the final vector.

What is the purpose of finding a unit vector in the context of vector scaling?

• To change the direction of the vector

• To find the angle between two vectors

• To scale the vector to a new magnitude

• To determine the vector's original magnitude

Which formula is used to calculate the magnitude of a vector?

• Sum of the vector components

• Square root of the sum of the squares of the components

• Product of the vector components

• Difference between the vector components

What is the first step in finding the unit vector of a given vector?

• Divide the vector by its magnitude

• Multiply the vector by its magnitude

• Add the vector components

• Subtract the vector components

How do you obtain a vector with a new magnitude but the same direction as the original?

• Subtract the unit vector from the original vector

• Add the original vector to the unit vector

• Divide the original vector by the new magnitude

• Multiply the unit vector by the new magnitude

What are the final components of the new vector with a magnitude of 9 and the same direction as (2, 5)?

• (18, 45)

• (18/sqrt(29), 45/sqrt(29))

• (9/sqrt(29), 5/sqrt(29))

• (2/sqrt(29), 5/sqrt(29))