MHT CET202019 Oct 2020Morning ShiftMathematicsVector AlgebraActual

If the points A (2,1,-1), B (0,-1,0), C (4,0,4) and D (2,0, x) are coplanar, then x=

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Correct answer

B. 1

Step-by-step solution

(B) aligned AB &=-2 i -2 j + k AC &=2 i - j +5 k AD &=- j +( x +1) k aligned Since the points A, B, C, D are coplanar, we write aligned & | array ccc -2 & -2 & 1 2 & -1 & 5 0 & -1 & x+1 array |=0 &-2[(-1-x)-(-5)]+2[(2 x+2)-0]+1[-2-0]=0 &-2[-1-x+5]+2[2 x+2]+[-2]=0 -8+2 x+4 x+2=0 x=1 aligned

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