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The value of lambda, for which the four points 2hati+3hatj-hatk, hati+3hatk, 2hati+4hatj-2hatk, hati-6hatj+lambda hatk are coplanar, is |
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Answer» 2 `C=3hat(i)+4hat(j)-2hat(k)` and `D=hat(i)-6hat(j)+lambda hat(k)` Now, `AB=-hat(i)-5hat(j)+4hat(k), AC =hat(i)+hat(j)-hat(k)` and `AD=-hat(i)-9hat(j)+(lambda+1)hat(k)` These will be coplanar, if `[(AB,AC,AD)]=0` `:. |(-1,-5,4),(1,1,-1),(-1,-9,(lambda+1))|=0` `implies -1(lambda+1-9)+5(lambda+1-1)+4(-9+1)=0` `implies 4lambda -24 =0` `implies lambda =6` |
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