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: Find ||v||.

Graph showing points (-21, 10) and (-21, -20) with a vector b between them.

Accepted Answer

Welcome back. I am so glad you're here. We're told for the given vector B find the magnitude. And we are given a graph on the graph. We have a vertical Y axis, a horizontal X axis. They come together at the origin in the middle. And then in quadrants two and three, we have a vector. For the initial side of our vector, the X and Y coordinates are negative 21 10. We can label those our X sub one Y sub one. And for the terminal side of our vector, we have an X value of negative 21 A Y value of negative 20. And we can label that our X sub two Y sub two. Our answer choices are answer choice, a 10 answer, choice B 20 answer choice C answer choice D 30. All right. So to find the magnitude of our vector B, we recall from previous lessons, that magnitude is the length of a vector. So we can find that by using the distance formula, the distance formula is the square root of now all underneath the radical, we have the quantity of X sub two minus X. Sub one squared plus the quantity of Y sub two minus Y sub one squared. Now we've already identified, identified our X sub ones and Y sub ones. So now let's just fill those in. We're taking the square of the quantity of X sub two is negative minus X sub one is also negative 21. And then we'll need to square that plus the quantity of our Y sub two is negative 20 minus our Y sub one is 10 and then we'll need to square that. So for the first one underneath the radical, the first set of parentheses, we have negative 21 minus a negative 21 that's negative plus 21 that's zero. So zero squared, that's zero. So for that first thing that all comes to be zero and then that's plus now for our second set of parentheses under there negative 20 minus 10, that's negative 30. So we have negative 30 which needs to be squared. Drew that radical a bit too long. All right. So negative 30 squared is going to be a positive 900. So we have the square rut of zero plus 0 plus 900 is 900. So we have the square rut of 900 which we already know is a positive 30. And that makes sense. So our magnitude for our given vector is 30 we look at our answer choices and this matches with answer choice d well done. We'll catch you on the next one.

In Exercises 1–4, u and v have the same direction. In each exercise: Find ||v||.

Key Concepts

Vector Magnitude

Coordinate System

Direction of Vectors

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