Plane

Given : The vertices of tetrahedron are
P(-1, 2, 0), Q(2, 1, -3), R(1, 0, 1) & S(3, -2, 3)

%5Ctherefore

Volume of tetrahedron

%3D%20%5C%20%5Cfrac%7B1%7D%7B6%7D%20%5C%20%5B%5Cvec%7BPQ%7D%20%5C%20%5Cvec%7BPR%7D%20%5C%20%5Cvec%7BPS%7D%5D

Now,

%5Cvec%7BPQ%7D%3D(2%2B1)%5Chat%7Bi%7D%2B(1-2)%5Chat%7Bj%7D%2B(-3)%5Chat%7Bk%7D%3D3%5Chat%7Bi%7D-%5Chat%7Bj%7D-3%5Chat%7Bk%7D

Similarly,

%5Cvec%7BPR%7D%3D2%5Chat%7Bi%7D-2%5Chat%7Bj%7D%2B%5Chat%7Bk%7D

%5C%26%20%5C%20%5C%20%5C%20%5C%20%5C%20%5Cvec%7BPS%7D%3D4%5Chat%7Bi%7D-4%5Chat%7Bj%7D%2B3%5Chat%7Bk%7D

%5Ctherefore

Volume of tetrahedron

%3D%5Cfrac%7B1%7D%7B6%7D%20%5Cbegin%7Bvmatrix%7D%3Cbr%20%2F%3E3%20%26%20-1%20%26%20-3%5C%5C%3Cbr%20%2F%3E2%20%26%20-2%20%26%201%20%5C%5C%3Cbr%20%2F%3E4%20%26%20-4%20%26%203%20%5Cend%7Bvmatrix%7D%20%3D%5Cfrac%7B2%7D%7B3%7D

Chapter Questions
1 MCQs