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Matrix & Vector Problem : Find the area of the triangle with vertices...; Compute the volume of the tetrahedron with vertices...

(a) (i) Find the area of the triangle with vertices (t, t-2), (t+2. t+2). (t-3, t)
Does the area changes with t?

(ii) In a theorem of solid geometry, the volume of the tetrhedron is
1/3 (base area )x( height). Compute the volume of the tetrahedron with vertices A( -1, 2, 0), B=(3, 5, 1), C(0, 0, 1) and D=(4.-1, 3).

Hint :Use the modulus of determinant and take A as the reference point to compute the volume of parallepiped first.

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Area of a triangle and volume of a tetrahedron are calculated using matricx and vector geometry. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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