In Exercises 1–4, u and v have the same direction. In each exerci...

Question

In Exercises 1–4, u and v have the same direction. In each exercise:
Is u = v? Explain.

Accepted Answer

Or the given vectors A and B find out if A equals B where A and B have the same direction. And we notice here we have two vectors vector A vector B both pointing in the same direction. Possible answers being A equals B and A is not equals B. Now to solve this, we need to see if the magnitudes of these vectors are the same because we already have the same direction. As long as the magnitudes are the same, the vectors will be the same. So let's find the magnitudes of both of these vectors. You'll take vector a first. Now, since we have two points, the magnitude of vector A will just be the distance between those two points. The distance formula tells us our distance between two points is X two minus X one squared plus Y two minus Y one squared. So for our vector A, our magnitude will be the square root of X two minus X one squared or 15 minus negative 17 squared plus the difference between our Ys squared, 19 minus 15 squared. You would get the square root A 32 squared plus four quick. This gives us a square root of 10 40. Let's do the same for vector B back to the vector B will be the square root of 30 minus negative two squared plus 11 minus seven squared, which gives us a square root of 32 squared plus four squared or the square root of 10 40. Both the magnitudes are then the same. Since they also have the same direction, the answer to our problem is answer A A is equals to B OK. I hope they help you solve the problem. Thank you for watching. Goodbye.

In Exercises 1–4, u and v have the same direction. In each exercise: Is u = v? Explain.

Key Concepts

Vector Direction

Vector Equality

Scalar Multiplication

Watch next