1. Points A, B and C are the three vertices of a triangle in 3D space (Cartesian coordinate system). It is known that

AB= (3,6,1)BC= (0,-7,-4)CA= (-3,1,3)

(a) Is triangle ABC a right-angled triangle? Justify your answer.

[Note: A right-angled triangle is a triangle with one 90o internal angle.]

The Cartesian coordinates of Point A are (3, 4, 1).

(b) What are the Cartesian coordinates of Point C?

(c) Find a vector that is perpendicular to the plane that contains triangle ABC.

Another point, Point D, is in the same 3D space such that the vector is perpendicular to the plane that contains triangle ABC.

(d) Given thatAD= (34, a, b), determine the values ofaandb.