a) Find x such that the vectors (3,2,x) and (2x,4,x) are orthogonal. b) Find the direction...

 

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a) Find x such that the vectors (3,2,x) and (2x,4,x) are orthogonal. b) Find the direction cosines and direction angles of the vector a=3i-2j-3k. Give the direction angles correct to the nearest degree. c) Consider the parallelepiped with edges AB, AC and AD, where A(1,0,1), B(4,1,3), C(5,a,2) and D(2,2,5). Find the real number, a > 0 such that the volume of the parallelepiped is 45 units. a) Find x such that the vectors (3,2,x) and (2x,4,x) are orthogonal. b) Find the direction cosines and direction angles of the vector a=3i-2j-3k. Give the direction angles correct to the nearest degree. c) Consider the parallelepiped with edges AB, AC and AD, where A(1,0,1), B(4,1,3), C(5,a,2) and D(2,2,5). Find the real number, a > 0 such that the volume of the parallelepiped is 45 units.