Let a,b,c be distinct $$non-negative$$ numbers. If the vectors $$ai^+aj^+ck^$$,$$i^+k^$$ and $$ci^+cj^+bk^$$ lie in a plane, then c is :

Question

Let a,b,c be distinct $$non-negative$$ numbers. If the vectors $$ai^+aj^+ck^$$,$$i^+k^$$ and $$ci^+cj^+bk^$$ lie in a plane, then c is :

Infinity Learn · Accepted Answer

Vectors in the same plane, hence a   a   $$c1$$   $$0$$    $$1c$$   c    b  $$=$$   $$0$$−$$1$$ (ab$$ − $$c2)  − $$1$$ (ac$$ − $$ac)  $$=$$  $$0$$                                                   $$c2$$  $$=$$  ab

$Let a, b, c be distinct non-negative numbers. If the vectors$ $a \hat{i} + a \hat{j} + c \hat{k}, \hat{i} + \hat{k} and c \hat{i} + c \hat{j} + b \hat{k} lie in a plane, then c is :$

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Let a,b,c be distinct non-negative numbers. If the vectors ai^+aj^+ck^,i^+k^ and ci^+cj^+bk^ lie in a plane, then c is :

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$Let a, b, c be distinct non-negative numbers. If the vectors$ $a \hat{i} + a \hat{j} + c \hat{k}, \hat{i} + \hat{k} and c \hat{i} + c \hat{j} + b \hat{k} lie in a plane, then c is :$