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
6→a−→c+λ(2→c−→a)=→a−→c+μ(→a+3→c)
5→a+2λ→c−λ→a=μ→a+3μ→c
Equating the coefficients of →a and →c, we get
5−λ=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.