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 = i - j

Accepted Answer

Welcome back everyone in this problem. Given the following vector V obtained a unit vector that aligns with the direction of VV equals negative I minus root three J A says the unit vector is negative quarter I plus root three divided by four JB says it's negative half I minus root three divided by two JC, negative half I plus root three divided by two J and D negative quarter I minus root three divided by four J. Now what do we know that can help us to figure out the unit vector? Well, recall that the unit vector that aligns in the same direction of a vector V is going to be equal to the vector V divided by its magnitude. That is in this case, the magnitude of V. So to figure out our unit vector first, we'll need to find the magnitude of V then divide the entire vector that is each component by that magnitude. Now, the magnitude of V OK is going to be equal to the square root of the sum of the squares of these components. So that's the square root of negative one squared plus negative root three squared. OK. Now we know that negative one squared equals one and negative root three squared is going to be equal to three and one plus three equals four. The square root of four equals two. Thus the magnitude of V is two. No, that we have its magnitude, we can find the unit vector because this now means that the unit vector is going to be equal to negative I, so that we know it's that would be one I so right, that's negative one, I divided by two minus the square root of three, divided by two J which simplifies the negative half I OK, minus root three divided by two J. Thus, this is the unit vector of V. If we look back on our answer choices, that means B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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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