In Exercises 39–46, find the unit vector that has the same dir...

Question

In Exercises 39–46, find the unit vector that has the same direction as the vector v.

v = 3i - 4j

Accepted Answer

Welcome back. I am so glad you're here. We're told, given the following vector V which is equal to 16, I minus 12 J obtain the unit vector that aligns with the direction of V. Our answer choices are answer choice A U equals 4/5 I minus 3/5 J. Answer choice B U equals 3/20 I minus 7/20 J. Answer choice C U equals 3/5 I minus 4/ J. And to answer choice, D U equals 16 5th I minus 12 5th J. All right, we recall from previous lessons that when we were finding a unit vector that will be equal to our vector divided by its magnitude and we know the vector. So our numerator is going to be 16, I minus 12 J. But what about the magnitude? Well, we recall from previous lessons that when A vector is given in terms of I and J, its magnitude is equal to the square rut of A squared plus B squared where A is the coefficient of I and B is the coefficient of J. So solving for our vector's magnitude A, the coefficient of I is 16 and then we'll square that plus B which is the coefficient of J is negative 12 and we'll square that all of that's underneath the radical. So now 16 squared is plus negative 12 squared is and 256 plus 144 is 400. So we're taking the square rut of 400 which is 20. So our denominator is 20. Now we can split this into two fractions to match our answer choices. So we'd have 16, divided by 20 I minus 12, divided by 20 J. And everything here is divisible by four. So the coefficient of I is going to be 4/5. So we have 4/5 I minus and the coefficient of J is going to be 3/5. And this is our unit vector. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

In Exercises 39–46, find the unit vector that has the same direction as the vector v.
v = 3i - 4j

Key Concepts

Vector Components and Notation

Magnitude of a Vector

Unit Vector and Normalization

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