In a frame of three-dimensional space, the coordinates of the points O, A, B and C as well as vector ū are: 0= (0,0,0) A=

Question

In a frame of three-dimensional space, the coordinates of the points O, A, B and C as well as vector ū are:
0= (0,0,0)
A= (1,2,3)
B= (8,6,7)
C= (-2,1, 8)
ū = (-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 ū.
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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