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 = i + j

Accepted Answer

Welcome back. I am so glad you're here. We're told, given the following vector where our vector is equal to five I plus J obtain the unit vector that aligns with the direction of V. Our answer choices are answer choice A U equals five square at 26 divided by 26 I plus square at 26 divided by J. Answer choice B U equals square divided by five I plus square root 26 divided by J. Answer trace C U equals five divided by I plus one divided by J. And answer choice D U equals I minus 26 J. All right. So to find a unit vector, we recall from previous lessons that we are going to take our vector and divide it by its magnitude and we're given our vector. So our unit vector equals in the numerator, our vector is five I plus J and that's divided by now. For the denominator, we need to know the magnitude of our vector. And we recall from previous lessons that the magnitude of our vector when it's given in terms of I and J is equal to the square of A squared plus B squared where A is going to be the coefficient of I and B is the coefficient of J. So here, our coefficient of I, our A term is five. So inside the radical, we have five squared plus and our B, the coefficient of J, that's just an unwritten one. So one squared inside the radical five squared is 25 plus one squared is 1 plus one is 26. We have the square rot of 26 that is our magnitude of our vector. So that goes in our denominator, the square rut of 26. And now it's just a matter of simplifying it. We don't want to have that radical in the denominator. So we rationalize it by multiplying both the numerator and the denominator by the square root of 26. And so we can distribute that to our numerator. We'll have five square root 26 I plus square root 26 J all divided by and square at 26 multiplied by square at 26 is just 26 in the denominator. And now that's fine, but we can also separate this into two separate fractions. So we can have five square at 26 divided by 26 I plus square at 26 divided by J. And that's just fine too. And that's the one that matches with our answer choice. We look at those answer choices and it 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 = i + j

Key Concepts

Unit Vector

Magnitude of a Vector

Direction of a Vector

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