In Exercises 5–12, sketch each vector as a position vector and find its magnitude. v = 3i + j

Video transcript

Draw the following vector and consider the origin as its initial point, then calculate its magnitude. But we have vector V equals 12 I plus three J. Now let's see if we can draw this vector. We're given a coordinate plane and we have a vector in the form A I plus B J. Since we're starting at the origin, our vector will go from 00 to the point A B where A B is our terminal point. Now based on our vector, we can find A and B our A will be 12. Our B will be three based on our formula. This seems our vector points in the direction of the 0. three. We can now draw this on our graph. Since we're starting at the origin, we will start at 00, then we will draw another point at the 0.12 three which is approximately and quadrant one a little bit higher than the X axis. Now, I can just connect the two points with the line and withdraw an arrow at the very end of the vector that gives us our vector drawn on the coordinate plane. Now let's calculate the magnitude the magnitude will be given by the square root of a squared plus B squared. We have the square root of 12 squared plus three square, which gives us the square root of 153. Now, we can simplify this where 1 53 breaks down to nine multiplied by 17, which gives us three square roots of 17. We can't simplify any farther. So our magnitude is just three squared to 17. Ok. I hope to help you solve the problem. Thank you for watching. Goodbye.