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 initial problem that needs to be solved regarding vector V?

• Finding a vector with a magnitude of 9 in the opposite direction of 7i + 3j

• Finding a vector with a magnitude of 9 in the same direction as 7i + 3j

• Finding a vector with a magnitude of 7

• Finding a vector with a magnitude of 3

Why does vector W not have a magnitude of 9?

• Because its components are too small

• Because it is already a unit vector

• Because its magnitude is the square root of 58

• Because it is not in the correct direction

What is the purpose of converting a vector into a unit vector?

• To simplify its components

• To make its magnitude equal to 1

• To increase its magnitude

• To change its direction

How do you calculate the unit vector of W?

• By multiplying its components by 9

• By adding 7 and 3

• By dividing its components by its magnitude

• By subtracting 3 from 7

What is the next step after finding the unit vector to get vector V?

• Subtract 9 from each component

• Multiply the unit vector by 9

• Add 9 to each component

• Divide the unit vector by 9

What is the final form of vector V in terms of its components?

• 9/sqrt(58), 3/sqrt(58)

• 27/sqrt(58), 63/sqrt(58)

• 7/sqrt(58), 3/sqrt(58)

• 63/sqrt(58), 27/sqrt(58)

What is the key takeaway when finding a new vector with a different magnitude?

• Convert to a unit vector and then multiply by the desired magnitude

• Change the direction first

• Divide by the desired magnitude

• Always add the magnitudes