Shikher studied about the three-dimensional geometry in his mathematics class. After the class while observing the view outside his class's window he observed top of a tower, foot of a tree and a boy sitting on a bench in the nearby park. He noticed that all the three things if considered as points in a 3-D plane then A(5.4, 3), B(6, 1, 1) and C(6.4) 10) are the positions of the top of the tower, foot of the tree and the boy sitting on the bench respectively in the 3-D plane. Also he considered his own position at point (4.5, 6) in the plane parallel to the plane where the three objects lie.
Based on the above information, answers the following questions:
(a) What is the cartesian equation of the plane passing through the position of all the three object observed by Shikher?
(b) What is the intercept form of the plane passing through the position of all the three objects observed by Shikher?
(c) What is the distance between Shikher and the plane passing through the positions of all the three objects?
(d) Find the direction cosines of the line passing through the positions of the top of the tower and the foot of the tree.
