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Question
Show that the following set of point are collinear ?
(2,3,−4),(−1,0,5),(3,4,−7)
(2,3,−4),(−1,0,5),(3,4,−7)
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Solution
Let the given points are
A(2,3,−4),B(−1,0,5),C(3,4,−7)
Then,
−−→AB=−−→OB−−−→OA=−3^i−3^j+9^k−−→BC=−−→OC−−−→OB=4^i+4^j−12^k−−→AC=−−→OC−−−→OA=^i+^j−3^k∣∣∣−−→AB∣∣∣=√(−3)2+(−3)2+(9)2=3√11∣∣∣−−→BC∣∣∣=√(4)2+(4)2+(−12)2=4√11∣∣∣−−→AC∣∣∣=√(1)2+(1)2+(−3)2=√11
Since,
|→BC|=|→AB|+|→AC|
Therefore, given points are collinear.
A(2,3,−4),B(−1,0,5),C(3,4,−7)
Then,
−−→AB=−−→OB−−−→OA=−3^i−3^j+9^k−−→BC=−−→OC−−−→OB=4^i+4^j−12^k−−→AC=−−→OC−−−→OA=^i+^j−3^k∣∣∣−−→AB∣∣∣=√(−3)2+(−3)2+(9)2=3√11∣∣∣−−→BC∣∣∣=√(4)2+(4)2+(−12)2=4√11∣∣∣−−→AC∣∣∣=√(1)2+(1)2+(−3)2=√11
Since,
|→BC|=|→AB|+|→AC|
Therefore, given points are collinear.
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