Learn How to Find the Unit Vector of a Given Vector as a Linear Combination

The video tutorial explains how to express vectors in component form and introduces unit vectors. It covers the calculation of vector magnitude and demonstrates how to find a unit vector by dividing the vector by its magnitude. The lesson concludes with a summary of the key concepts discussed.

What is the component form of a vector if it is given as a linear combination of i and j?

• The product of the coefficients of i and j

• The coefficients of i and j written as a pair

• The sum of the coefficients of i and j

• The difference between the coefficients of i and j

What is the purpose of finding a unit vector?

• To maintain the direction but change the magnitude to one

• To find a vector with a magnitude of zero

• To increase the magnitude of the vector

• To change the direction of the vector

How do you calculate the magnitude of a vector W = (1, -2)?

• By taking the square root of the sum of the squares of the components

• By adding the components

• By multiplying the components

• By subtracting the components

What is the unit vector of W = (1, -2) after dividing by its magnitude?

• (1/√5, -2/√5)

• (√5, -√5)

• (2, -1)

• (1, -2)

Why is it important to leave the answer with a radical on the bottom?

• To ensure the vector is in standard form

• To make it easier to graph

• To maintain the exact value

• To simplify the calculation