If az_1+bz_2+cz_3=0 for complex numbers z_1,z_2,z_3 and real numbers a,b,c, then z_1,z_2,z_3 lie on a

JEE Main Mathematics question

If for complex numbers and real numbers , then lie on a

(A)Straight line
(B)Circle
(C)Depends on the choice of Correct
(D)None of these

Answer: (C)

Solution

Three vectors in the plane always satisfy some real linear relation, so the condition by itself does not force the points to lie on a line or a circle. If additionally

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Question ID VK-013922