In Exercises 22–24, sketch each vector as a position vector an...

Question

In Exercises 22–24, sketch each vector as a position vector and find its magnitude.

v = -3j

Accepted Answer

Hello, today we're going to be drawing the following vector on an axis. Then we're going to be calculating the vector's magnitude. So let's go ahead and start by graphing the vector. We're first going to start by drawing an axis. Now one thing to note is that the I components represent the X axis and the J components represent the Y axis. Now the given vector is V is equal to negative five I. Now one thing to note about the vector is that we are not given AJ component. We can include that J component by giving it a coefficient of zero. So what this means is that the X value of the vector is going to be negative five and the Y value of the vector is going to be zero. That means that the end of this vector will be located at negative five comma zero. So we're going to graph negative five comma zero on our axis and the vector is going to start at the origin and end at this point. So this is going to be the rough graph of the given vector. Now that we've graphed the vector, we're going to calculate the magnitude of the vector. Now, the magnitude of the vector is defined as the square root of the sum of its components squared. So we know that the I component is negative five and we know that the J component is zero. So the magnitude of vector V is equal to the square root of negative five squared plus zero squared, negative five squared will give us the value of positive 25 and zero squared will give us the value of zero 25 plus zero will give us the value of 25. So we have the square root of 25 and the square root of 25 will simplify to give us the value of five. So that means the magnitude of V is going to have a magnitude of five and this is going to be the answer to the given problem. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 22–24, sketch each vector as a position vector and find its magnitude.
v = -3j

Key Concepts

Position Vector

Vector Components and Unit Vectors

Magnitude of a Vector

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