AP EAMCET202420 May 2024Evening ShiftMathematicsVector AlgebraActual

If the points having the position vectors - i +4 j -4 k , 3 i +2 j -5 k ,-3 i +8 j -5 k and -3 i +2 j + k are coplanar, then =

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Correct answer

C. -2

Step-by-step solution

Let OA =- i +4 j -4 k ; OB =3 i +2 j -5 k aligned & OC =-3 i +8 j -5 k and OD =-3 i +2 j + k & AB =4 i -2 j - k , AC =-2 i +4 j - k & AD =-2 i -2 j +( +4) k aligned For coplanar [ AB AC AD ]=0 aligned & | array ccc 4 & -2 & -1 -2 & 4 & -1 -2 & -2 & +4 array |=0 & 4(4 +16-2)+2(-2 -8-2)-1(4+8)=0 & 12 +24=0 =-2 aligned

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