WBJEE · Maths · Vector Algebra
Let \(\vec{\alpha}, \vec{\beta}, \vec{\gamma}\) be three non-zero vectors which are pairwise non-collinear. If \(\vec{\alpha}+3 \vec{\beta}\) is collinear with \(\vec{\gamma}\) and \(\vec{\beta}+2 \vec{\gamma}\) is collinear with \(\vec{\alpha}\), then \(\vec{\alpha}+3 \vec{\beta}+6 \vec{\gamma}\) is
- A \(\vec{\gamma}\)
- B \(\overrightarrow{0}\)
- C \(\vec{\alpha}+\vec{\gamma}\)
- D \(\vec{\alpha}\)
Answer & Solution
Correct Answer
(B) \(\overrightarrow{0}\)
Step-by-step Solution
Detailed explanation
\(\vec{\alpha}+3 \vec{\beta}=\mathrm{k}_{1} \vec{\gamma} \Rightarrow \vec{\beta}=\frac{\mathrm{k}_{1}}{3} \vec{\gamma}-\frac{\vec{\alpha}}{3}\) \(\vec{\beta}+2 \vec{\gamma}=\mathrm{k}_{2} \vec{\alpha} \Rightarrow \vec{\beta}=\mathrm{k}_{2} \vec{\alpha}-2 \vec{\gamma}\)…
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