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Consider the lines given by L_(1):x+3y-5=0 L_(2):3x-ky-1=0 L_(3):5x+2y-12=0 Match the following lists. |
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Answer» `L_(1): x+3y-5 = 0` `L_(2): 3x-ky-1 = 0` `L_(3): 5x+2y-12 = 0` `L_(1) " and " L_(3)` intersect at (2, 1) `therefore L_(1), L_(2), L_(3)` are concurrent if 6-k-1 = 0 or k=5 `"For " L_(1), L_(2)` to be parallel `(1)/(3) = (3)/(-k) RARR k = -9` `"For " L_(2), L_(3)` to be parallel `(3)/(5) = (-k)/(2) rArr k = (-6)/(5)` Thus, for k = 5, lines are concurrent and for `k = -9, (-6)/(5),` at least two lines are parallelk. So, for these values of k, lines will not FORM triangle. Obviously, for `k ne 5, -9, (-6)/(5),` lines form triangle. |
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