ANSWER ALL QUESTIONS CORRECTLY. PROVIDE SOLUTIONS AND ALSO ILLUSTRATIONS FOR ITEMS WITH ASTERISK BEFORE THE ITEM NUMBER. UPLOAD YOUR SOLUTIONS IN THE APPROPRIATE SECTION.

1) Find the unit vector. The given vector is: A = 5i + 4j + 3k. Rationalize * 4 points your final answer. (No radicals on the denominators.) Also, prove that it is a unit vector. V2 2v2 3v2 V2 2v2 3v2 2 k 5 10 2 + k 5 5 O Option 1 Option 2 2) Find the dot product of the given vectors. The given vectors are: A = 5i + * 4 points 4j + 3k & B = 3i + 4j + 5k. Use the Dot Product Method on the vectors given in vector notation. Rationalize your final answer. (No radicals on the denominators.) 46 64*3) Find the magnitude of the cross product of the two vectors given and * 4 points the angle between them. The given vectors are: A = 5i + 4j + 3k & B = 3i + 4j + 5k. Use the Determinant Method to solve for the magnitude. Apply the Cross Product Theorem to solve for the angle. Rationalize your final answer. (No radicals on the denominators.) 8i - 16j + 8k ; 23 degrees 81- 16j + 8k ; 67 degrees *4) Using a powerful airgun, a steel ball is shot vertically upward with a * 4 points velocity of 262 ft/s, followed by another shot after 5 seconds. Find the initial velocity of the second ball in order to meet the first ball 492 feet from the ground. 201 fps 61 fps*5) A flywheel 15 cm in diameter accelerates uniformly from rest to 500 * 4 points rpm in 120 seconds. Calculate the angular acceleration. 0.436 rad/ sec 2.62 rad/ sec O Option 1 Option 2