In a frame of three-dimensional space, the coordinates of the points O, A, B and...

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Calculus

In a frame of three-dimensional space, the coordinates of the points O, A, B and C as well as vector ? are:0= (0,0,0)A= (1,2,3)B= (8,6,7)C= (-2,1, 8)? = (-3.4, -1)a) Determine the angle formed between the vectors AB and AC.b) Determine the coordinates of point P located 3 units from point A on segment AB.c) Find the coordinates of a point Q such that the vector AQ is parallel to the vector ?.d) Find the centroid of A, B and C.e) Find the volume of the tetrahedron OABC.f) Determine the normal equation of the plane containing the points A, B and C.

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In a frame of three-dimensional space, the coordinates of the points O, A, B and C as well as vector ? are:0= (0,0,0)A= (1,2,3)B= (8,6,7)C= (-2,1, 8)? = (-3.4, -1)a) Determine the angle formed between the vectors AB and AC.b) Determine the coordinates of point P located 3 units from point A on segment AB.c) Find the coordinates of a point Q such that the vector AQ is parallel to the vector ?.d) Find the centroid of A, B and C.e) Find the volume of the tetrahedron OABC.f) Determine the normal equation of the plane containing the points A, B and C.