I have no idea how my teacher gets the answer for "Example 2.4". Honestly, I am terrible at physics and Vector stuff.

So,please take your time to explain in detail to me how my teacher gets the answer for the question below, using more calculation,less wording and more tabling or drawing explanations!

Example 2.4:

Example 2.4 IN F = 450 N Given: The screw eye is subjected to two forces, F, and F2 . 450 Find: The magnitude and the coordinate direction angles of the resultant force. Plan: F2 = 600 N 1) Using the geometry and trigonometry, resolve and write F, and F, in the Cartesian vector form. 2) Add F, and F, to get FR . 3) Determine the magnitude and angles a, B, Y .Example 2.4 Fi=450N i First resolve the force F, . F,, = 450 sin45 = 3182 N F' = 450 cos45 = 3182N ' \\. F' can be further resolved as, ' F, =318.2sin30=159.1 N F;, = 318.2cos 30 = 275.6 N Now, we can write: F,={-159i + 276j+318 k} N Example 2.4 F,= 450N Now, resolve force F,. First, we need to find the value of y. cos 2(45%) +cos2(60) +cos2(y) = 1 S Solving, we get y = 120 The force F, can be represented in the Cartesian vector form as: F,=600{ cos 45i +cos 60j+cos 120k } N ={4243i +300 j 300k } N F,={424i + 300 j300 k} N Example 2.4 F = 450 N So FR= F1 + F2 and 450 F1 = {- 159.1 i + 275.6 j + 318.2 k } N Jary 459 F, = { 424.3 i + 300 j - 300 k } N F, = 600 N FR= { 265.2 i + 575.6 j + 18.20k } N Now find the magnitude and direction angles for the vector. FR = (265.2 2 + 575.6 2 + 18.20 2) 1/2 = 634.0 = 634 N a = cost! (FRX / FR) = cos-1 (265.2 / 634.0) = 65.30 B = cos- (FRy / FR) = cos-1 (575.6 / 634.0) = 24.80 y = cost (FR2 / FR) = cos-1 (18.20 / 634.0) = 88.40