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Question

Statement-1: If vectors ¯¯¯a and ¯¯c are non collinear then the lines ¯¯¯r=6¯¯¯a¯¯c+λ(2¯¯c¯¯¯a) , ¯¯¯r=(¯¯¯a¯¯c)+μ(¯¯¯a+3¯¯c) are coplanar.
Statement-2: There exist λ and μ such that the two values of ¯¯¯r become same.

A
Statement-1 is true, statement-2 is true 1 statement-2 is correct explanation for statement-1.
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B
Statement-1 is true, statement-2 is true, statement-2 is not correct explanation for statement-1.
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C
Statement-1 is true, statement-2 is false.
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D
Statement-1 is false, statement-2 is true
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Solution

The correct option is A Statement-1 is true, statement-2 is true 1 statement-2 is correct explanation for statement-1.
Since a and c are not collinear, we can equate the coefficients to find μ and λ
Equating r
6ac+λ(2ca)=ac+μ(a+3c)
5a+2λcλa=μa+3μc
Equating the coefficients of a and c, we get
5λ=μ ......... (1)
2λ=3μ ...... (2)
Solving equations (1) and (2), we get
λ=3 and μ=2
Hence, statement 1 and 2 are true and statement 2 is correct explanation for statement 1.

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