triangle abc has vertices at a(-3,1),b(-3,4) abd c(-7,1)

4. Use vector methods to find the area of a triangle with the vertices (1,-1,2), (-2,1,1), (1,2,3). Find a unit vector which is perpendicular to the plane containing this triangle.

Determine whether u = [2, 4, -8] and upsilon = [5, 3, 7] make an acute angle, an obtuse angle, or are orthogonal. Give an approximation in degrees for the angle theta between those two vectors. b) Use the scalar product and the norm to prove that the triangle with vertices A(1, 0, 1), B(1, 1, 1) and C(1, 1, 0) is a right isosceles triangle. At which vertex is the right angle? c) Given the triangle with vertices A(1, 0, -1), B(2, 3, 2) and C(-1, -2, 1), find the cosine of its internal angle theta at vertex C.