A) 0
B) 2
C) \[-\,\,1\]
D) 1
Correct Answer: D
Solution :
Here \[{{x}_{1}}=-1,\]\[{{x}_{2}}=2,\]\[{{x}_{3}}=5\]and \[{{y}_{1}}=3,\]\[{{y}_{2}}=k\]and \[{{y}_{3}}=-1.\] Now, \[\Delta =0\]\[\Leftrightarrow \]\[{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})=0\] \[\Leftrightarrow \]\[-1.(k+1)+2(-1-3)+5(3-k)=0\] \[\Leftrightarrow \]\[-k-1-8+15-5k=0\]\[\Leftrightarrow \]\[6\]\[\Leftrightarrow \]\[k=1.\] Hence, \[k=1.\]You need to login to perform this action.
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