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

Question

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

v = 6i

Accepted Answer

Welcome back. I am so glad you're here. We are told, given the following vector V where V is equal to 13, I obtain the unit vector that aligns with the direction of V. Our answer choices are answer choice, A U equals 13, I answer choice B U equals I answer choice C U equals I divided by 13. And answer choice D U equals 169 I. All right, we recall from previous lessons that when we're finding the unit vector that's going to be our vector divided by its magnitude and we know our vector. So in the numerator we have 13 I, but what about its magnitude? Will we recall from previous lessons that when our vector is given in terms of I and J, its magnitude is found by taking the square rut of A squared plus B squared where A is the coefficient of I and B is the coefficient of J. So for this particular vector, our for our A squared, the A, the leading co fish or excuse me, the co fission of I is 13. So we're taking the square it of 13 squared plus B, the coefficient of J Well, we have no J term. So there are zero J S so B is zero. So that will be zero squared and we'll take the square ret of 13 squared is 169 plus zero squared is zero. So it's just the square ret of 169 which we know is 13. So our denominator is 13. Now, we can simplify this 13 I divided by 13 that just equals one I or just I. So here, our unit vector is equal to I, we look at our answer choices and that matches with answer choice. B 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 = 6i

Key Concepts

Unit Vector

Magnitude of a Vector

Vector Notation

Watch next