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

Question

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

v = -3i - 4j

Accepted Answer

Hello, today we're going to be graphing the following vector. Then we're going to calculate the magnitude of the vector. So we're first going to start by drawing an axis. Now one thing to note about the axis is that the I components of the vector represent the X axis and the J components of the vector represent the Y axis. The vector that is given to us is V is equal to negative five I plus 12 J. What this means is that the vector will be traveling negative five units in the X direction and will be traveling 12 units in the Y direction. So the vector is going to travel to negative five and then up to nag to positive 12. So the vector is going to end at the point negative five comma 12. Now when we graph a vector, the vector will start at the origin and end at the indicated point. So we're going to draw a line connecting the two dots, then we're going to draw an arrow at the end of the line at negative five comma 12. This is going to be the graphical representation of the given vector. Now that we've graphed the vector, we're going to calculate the vector's magnitude. Now, in order to calculate the magnitude of a vector, we're going to be taking the square root of the sum of its components squared. So we know that the value of I or X in this case is negative five. And we know that the value of J or Y is equal to 12, that means the magnitude of V is equal to the square root of negative five squared plus 12 squared, negative five squared will simplify to give us the value of positive 25 and 12 squared will simplify to give us the value of positive 144. Finally 25 plus 1 44 will give us the value of 169. So we have the square root of 169 which will simplify to give us the value of 13. That means the magnitude of vector V is going to equal to and this will 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.

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In Exercises 22–24, sketch each vector as a position vector and find its magnitude. v = -3i - 4j