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Assertion (A): If vectors a and c are non-collinear, the lines r = 6a - c + lambda*(2c - a) and r = a - c + mu*(a + 3c) are coplanar. Reason (R): There exist values of lambda and mu such that the two position vectors in Assertion (A) become equal.

1. A is true, R is true and R is correct explanation of A
2. A is true, R is true, R is not correct explanation of A
3. A is true, R is false
4. A is false, R is true

Correct answer: A is true, R is true and R is correct explanation of A

Solution

Set 6a-c+lambda*(2c-a) = a-c+mu*(a+3c). Coefficient of a: 6-lambda = 1+mu => lambda+mu=5. Coefficient of c: 2*lambda-1 = 3*mu-1 => 2*lambda=3*mu. Solving: lambda=3, mu=2. Lines intersect at this point => coplanar. R correctly explains A.

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