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

v = 4i - 2j

Video transcript

Given the following vector V, obtain the unit vector that aligns with the direction of V, where V is the vector -5 I plus 2J. And we have 4 possible unit vectors as answers. Now, to solve this, we first need to find the magnitude of vector V. The magnitude is a square root of the sum of our components squares. So we can write that as the square root of our first component, -5 squad, plus our second component 2 squared. We can now simplify, -5 squared is 25. 2 squared is 4. Which gives us the square root of 29. Now the square of 29 does not simplify, so we'll just leave it. Now, we can find our unit vector. Our unit vector is our current vector divided by its magnitude. Which in our case, we have 5 I plus 2J. Divided by the square root of 29. We can now simplify -5 divided by a square root of 29 I. Plus 2 divided by the square root of 29. J Now, we also don't want radicals in our denominator, so let's rationalize the denominator. We will multiply. Both components by the square root of 29 divided by the square root of 29. This simplifies to -5 square roots of 29. But about 29 I. Plus 2 square roots of 29 divided by 29 j. This is now a simplified unit vector. Which means we can see the answer to our problem. I answer C. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.