Draw a cube and Cartesian axes. All points of the cube lie in the (+,+,+) octant

Question

Draw a cube and Cartesian axes. All points of the cube lie in the (+,+,+) octant of the coordiante system. One vertex of the cube is at (0,0,0), the point called O. The vertex that is diagonally across from O on the square in the xz plane is point A. The vertex that is diagonally across from O on the square in the yz plane is point B. The vertex that is diagonally across the cube from O is called C. (a) Determine the angle (in degrees) between the vectors OA and OB. (b) Determine the angle (in degrees) between the vectors OA and OC.

Explanation / Answer

let the lenght of each side be a; OA = 2^0.5*a =OB =AB OAB form equilateral triangle. so angle between OA andOB is 60 degrees. b) AC=a; OC= v3*a; OA= v2*a, triangle oac is right angle at point A, angle between OA and OC is sin^-1(1/v3) i.e. 35.2644 degree

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