InterviewSolution
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InterviewSolution
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Consider the system of equations `a_(1) x + b_(1) y + c_(1) z = 0` `a_(2) x + b_(2) y + c_(2) z = 0` `a_(3) x + b_(3) y + c_(3) z = 0` If `|(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =0`, then the system hasA. Statement -1 is True , Statement - 2 is true , Statement- 2 is a correct explanation for statement - 4B. Statement-1 is True , Statement-2 is True , Statement -2 is not a correct explanation for Statement - 1 .C. Statement-1 is True , Statement - 2 is False .D. Statement - 1 is False , Statement -2 is True . |
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Answer» Correct Answer - A The area of triangle formed by the lines `a_(1)x + b_(1) y + c_(1) = 0 , a_(2) x + b_(2)y + c_(2) = 0` and `a_(3) x + b_(3) y + c_(3) = 0` is `Delta = (1)/(2C_(1) C_(2)C_(3)) |{:(a_(1), b_(1), c_(1)), (a_(2) ,b_(2), c_(2)) , (a_(3), b_(3), c_(3)):}|^(2)` where `C_(1) , C_(2) , C_(3)` are cofactors of `c_(1) , c_(2) , c_(3)` respectively in the matrix `[{:(a_(1), b_(1), c_(1)), (a_(2) ,b_(2), c_(2)) , (a_(3), b_(3), c_(3)):}]` If the lines are concurrent , then `Delta = 0 implies |{:(a_(1), b_(1), c_(1)), (a_(2) ,b_(2), c_(2)) , (a_(3), b_(3), c_(3)):}|` = 0 So , statement -2 is true . Also , statement - 1 is true and statement - 2 is a correct explanation for statement -1 . |
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