National (3,6) (b) Now draw a vector F from the head of vector D at x = 13, y = 10 to x = 17, y = 19. On your graph paper show Fx and Fy. Draw the vector sum of D and F on your graph paper and call this sum vector H. Now see how you can draw vector H as the vector sum of the x and y components of vectors D and F that is as the sums of Dx and Fx, and Dy and Fy. (c) We will now indicate the length (magnitude) of any vector by writing it in non-bold face font, i.e. the magnitude of D is D so that Dx = Dx i etc. Calculate Hx and Hy in the terms of the x and y components of D and F. Now draw H in terms of Hx and Hy and on your graph, if you haven't done so already indicate where Hx and Hy are. (d) Note that Hx and Hy form two perpendicular sides of a right triangle with H as its hypotenuse. Using the Pythagorean theorem find the magnitude of H and using an appropriate trigonometric function find its angle. With your ruler and protractor measure the length and angle of H and compare them with your calculations. II) Vector addition can be done analytically, i.e. by manipulating numbers. We can see how this works by first recognizing that any vector can be written as the vector sum of vectors in the x, y and z directions. For simplicity we will work in only two dimensions. (a). Draw a vector, D starting from positions x = 3, y= 6 on your graph paper and ending at x = 13, y = 10. Now draw a vector Dx in the x direction from x = 3, y = 6 to x = 13, y = 6 and then another one Dy in the y direction, starting from the head of this last vector, from x = 13, y = 6 to x = 13 y = 10. How can we write (describe) D as a combination of Dx and Dy? Dx and Dy are called the x and y components of vector D. If we define a vector of length 1 in the x direction as i and one of length 1 in the y direction as j how can we write the x and y components of D, in terms of i and j?