In Exercises 31–32, find the unit vector that has the same direct...

Question

In Exercises 31–32, find the unit vector that has the same direction as the vector v.

v = -i + 2j

Accepted Answer

Given the following vector A obtain the unit vector that aligns with the direction of A, where we have A equals negative two I plus nine J. We have four different answers. All vectors in terms of I and J. Now to solve this, we need the formula for a unit vector where we have U as equals to our vector A divided by the magnitude of vector A. Let's find the magnitude of A. Now we know our vector A is in the form X I plus Y J which is just the form of a vector in terms of I and J. Our magnitude then will be the square root of X squared plus Y squared. Now we see our X should be negative two. So we have negative two square and our Y should be nine, which means we have nine squared. We have the square root of four plus 81 which is the square root of 85. We can plug this value into our unit vector. Are you the vector or B R vector negative two I plus nine J divided by the square root of 85 which can be split up as negative two divided by the square of 85 I plus nine, divided by the square of 85 J. Now we have a radical on the denominator and we can't really have that. So we have to rationalize our fractions to do this. We will multiply everything by the square root of 85 divided by the square root of 85. This gets rid of the radicals and the denominator, we will get negative two square roots of 85 divided by 85 I plus nine square roots of 85 divided by J. Which means this is our final unit vector. This means the answer to our problem is answer C negative two squared of 85 divided by 85 I plus nine squares of 85 divided by 85 J. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 31–32, find the unit vector that has the same direction as the vector v. v = -i + 2j

Key Concepts

Unit Vector

Magnitude of a Vector

Direction of a Vector

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