A) -2 and -1
B) -2 and 1
C) 2 and -1
D) 2 and 1
Correct Answer: D
Solution :
Since, position vectors of A,B, C are\[2\hat{i}-\hat{j}+\hat{k},\] \[\hat{i}-3\hat{j}-5\hat{k}\] and\[a\hat{i}-3\hat{j}+\hat{k},\]respectively. \[\therefore \]\[AC=(a\hat{i}-3\hat{j}+\hat{k})-(2\hat{i}-\hat{j}+\hat{k})=(a-2)\hat{i}-2\hat{j}\] and \[BC=(a\hat{i}-3\hat{j}+\hat{k})-(\hat{i}-3\hat{j}-5\hat{k})\] \[=(a-1)\hat{i}+6\hat{k}\] Since, the \[\Delta ABC\] is right angled at C, then \[AC.BC=0\] \[\Rightarrow \]\[\{(a-2)\hat{i}-2\hat{j}\}.\{(a-1)\hat{i}+6\hat{k}\}=0\] \[\Rightarrow \]\[(a-2)(a-1)=0\]\[\Rightarrow \]\[a=1\] and 2
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