lf there are three points A(2,3, 4), B(- 1,2, - 3) and C(-4,1, - 10) in a space, then they are

Given, points are A(2,3,4), B(-1,2, -3) and C(-4,1, -10).Now, determine area of triangleArea of triangle  Δ=Δxy2+Δγz2+Δzx2Where, Δxy=12x1    y1    1x2    y2    1x3    y3    1 , Δyz=12y1    z1    1y2    z2    1y3    z3    1  and Δzx=12z1    x1    1z2    x2    1z3    x3    1now,Δxy=12231−121−411=122(2−1)−3(−1+4)]+1(−1+8)=12|[2−9+7]|=0Δyz=123412−311−101=123(−3+10)−4(2−1)+1(−20+3)=12|21−4−17|=0Δzx=12421−3−11−10−41=124(−1+4)−2(−3+10)+1(12−10)=12|[12−14+2]|=0Δ=02+02+02=0Hence, given points are collinear