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Question

If ¯¯¯a and ¯¯b are two non-collinear vectors, then the points l1¯¯¯a+m1¯¯b, l2¯¯¯a+m2¯¯b and l3¯¯¯a+m3¯¯b are collinear if

A
l1(m2m3)=0
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B
l1(m1m3)=0
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C
l1(m1+m3)=0
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D
l1(m2+m3)=0
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Solution

The correct option is A l1(m2m3)=0
¯a and ¯b are non-collinear
=∣ ∣111l1l2l3m1m2m3∣ ∣=0
c1c1c2c3c1c3=∣ ∣010l1l2l2l1l3m1m2m2m1m3∣ ∣=0
=(l1l2)(m1m3)+(l1l3)(m1m2)=0
l1(m2m3)=0

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