Day 3 The next thing e wanted to try was to construct an escape room. So, he pondered, hmm, let's make the escape room a box so that it's width is 2 cm, it's length is 2 cm but it's height is 3 cm. What would such a box look like? a. Starting at the point, sketch A(1,2,3) using an x y z coordinate axes. [1 mark] b. Use the above information, ie the width and length of the box must be 2 units and the height of the box must be 3 units, determine the 8 points representing the vertices of the box. NOTE: the starting point of the box must be A(1,2,3). List the other points below: A( . . .) B( , , ,) C( . . .) D( . . .) E( . . .) l:( , , .) G( . . ,) H( . . .) c. Draw the above points. Do so with a ruler, equally spaced point and large enough to take up the space provided below. [2 marks] d. e wanted to hang a banner at the point where the two body diagonals met. Using (3,0,0) and (1,2,3) as the rst body diagonal and (3,2,0) and (1,0,3) as the other diagonal, i. Determine the vector equations of the two body diagonals Body Diagonal 1 Body Diagonal 2 [4 marks] ii. Using dot products, do the two body diagonals make a 90 degree angle with each other? If not, what acute angle do they make with each other? [2 marks] iii. Based on your vector equations, determine if the two lines representing the body diagonals meet. If they do meet, determine the coordinates. [4 marks] _, iv. Refer to your box: Form the vectors 3 = W2. and 13 = PR wheremP)' = (1,0,0), (00): (3,0,0) and (0H) = (1,2,0) Determine Q + 1? and Show this vector on your box. [3 marks] Determine Iii + l [1 mark] vi. Determine the angle between it and E + 13 by forming a triangle between vectors a, 13 and it + 13 and therefore creating a triangle and using the appropriate trig |aws(sine, cosine,trig ratios, Pythagoras) to determine this angle. [3 marks] Determine the numeric value of ii - (3 + 13) [2 marks]