PLEASE TRY TO SOLVE THE QUESTIONS WITH DETAILED STEPS.

Question 5 - Student 4 A cube is constructed from the three vectors 3, 3, and E", as shown below. H G a. Express each of the diagonals AGZ W, E, and W" in terms of ('1', 3, and E". b. Is LTG'I = lil? Explain. Question 3 - Student 3 3 of 6 Use the following diagram to show that each of the following is equal to PQ Show your reasoning (e.g. with a diagram and/or by mentioning the triangle/parallelogram law) (RQ + SR) + TS + PT R RQ + (SR + TS) + PT RQ + SR + (TS + PT) P Question 4 - Student 4 ABCDEFGH is a rectangular prism. a. Write a single vector that is equivalent to EG + GH + HD + DC. b. Write a vector that is equivalent to EG + GD + DE. A B H G FQuestion 1 - Student 1 Two vectors, 3 and 3, have a common starting point with an angle of 120 between them. The vectors are such that I'l = 3 and '3' = 4. a. Calculate '3 + 3|. b. Calculate the angle between If and If + 3. Question 2 - Student 2 > Three collinear vectors. 3, b. and Z", are such that If = %3 and 6' = %2". a. Determine integer values for m and n such that mi" + H]; = 0. How many values are possible for m and n to make this statement true? 13. Determine integer values for d, e, and f such that d3 + 63 + f2" : 6. Are these values unique