If a,b,c are non-coplanar vectors and `lamda` is a real number, then the vectors `a+2b+3c,lamdab+4c and (2lamda-1)c` are non-coplanar for

Question

If a,b,c are non-coplanar vectors and `lamda` is a real number, then the vectors `a+2b+3c,lamdab+4c and (2lamda-1)c` are non-coplanar for

If a,b,c are non-coplanar vectors and `lamda` is a real number, then the vectors `a+2b+3c,lamdab+4c and (2lamda-1)c` are non-coplanar for
A. all value of `lamda`
B. all except one value of `lamda`
C. all except two value of `lamda`
D. no value of `lamda`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
The three vectors (a+2b+3c),`(lamdab+4c) annd (2lamda-1)`c are non-coplanar, if
`|(1,2,3),(0,lamda,4),(0,0,2lamda-1)|ne0`
`implies (2lamda-1)(lamda) ne0`
`implies lamda ne0,(1)/(2)`
So, these three vectors are non-coplanar for all except two values of `lamda`.

4 views Answered 2023-02-05 15:29