If a _ 1 , a _ 2 and a _ 3 are non–coplanar vectors and (x + y – 3) a _ 1 + (2x – y + 2)…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
If \(\overrightarrow{\mathrm{a}}_{1}, \overrightarrow{\mathrm{a}}_{2}\) and \(\overrightarrow{\mathrm{a}}_{3}\) are non–coplanar vectors and
(x + y – 3) \(\overrightarrow{\mathrm{a}}_{1}+\)(2x – y + 2) \(\overrightarrow{\mathrm{a}}_{2}\)+ (2x + y + λ) \(\overrightarrow{\mathrm{a}}_{3}\) = \(\overrightarrow{0}\)
holds for some ‘x’ and ‘y’ then ‘λ’ is
(x + y – 3) \(\overrightarrow{\mathrm{a}}_{1}+\)(2x – y + 2) \(\overrightarrow{\mathrm{a}}_{2}\)+ (2x + y + λ) \(\overrightarrow{\mathrm{a}}_{3}\) = \(\overrightarrow{0}\)
holds for some ‘x’ and ‘y’ then ‘λ’ is
- \(\frac{7}{3}\)
- 2
- \(-\frac{10}{3}\)
- \(\frac{5}{3}\)
Answer
(C) - 10 3
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