Find the measure of the angle between the three-dimensional vectors a and b. Express the answer in radians rounded to two decimal places, if it is not possible to express it exactly. a = 2i − j − 8k,  b = v + w,  where v = −8i − 2j + 8k

Find the magnitude of V x W    (i.e. the magnitude of V cross W)

What is the angle (in radians) between the vectors 4.5i + 2.2j + 5.3k and 3i + 2j – 4k ? Round answer to two decimal places

N. The figure below shows a trajectory of a satellite that is launched from point A using a rocket, to point C in space, this movement AC took a certain time. Then it moved towards point B [angle ACB is 90 degrees] in 1.4 hours. At this moment of time, the distance between the launching point and the satellite measured in travelling hours, AB = 1.9 hours. The angle CAB = 50.0°. Write down the vectors CB and AB in terms of i and j components [Cartesian format]. Write down an equation relating AC, AB and CB as vectors, then find the vertical travelling duration points A and C, or the vector AC? [Hint: you can simplify the problem by rotating the triangle such that AC coincides with the y-axis] B A