JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\overrightarrow{ a }=2 \hat{ i }+\hat{ j }+\hat{ k }\), and \(\overrightarrow{ b }\) and \(\overrightarrow{ c }\) be two nonzero vectors such that \(|\vec{a}+\vec{b}+\vec{c}|=|\vec{a}+\vec{b}-\vec{c}| \quad\) and \(\vec{b} \cdot \vec{c}=0\). Consider the following two statement: \((A)\) \(|\overrightarrow{ a }+\lambda \overrightarrow{ c }| \geq|\overrightarrow{ a }|\) for all \(\lambda \in R\). \((B)\) \(\overrightarrow{ a }\) and \(\overrightarrow{ c }\) are always parallel
- A only \((B)\) is correct
- B neither \((A)\) nor \((B)\) is correct
- C only \((A)\) is correct
- D both \((A)\) and \((B)\) are correct.
Answer & Solution
Correct Answer
(C) only \((A)\) is correct
Step-by-step Solution
Detailed explanation
\(|\vec{a}+\vec{b}+\vec{c}|^2=|\vec{a}+\vec{b}-\vec{c}|^2\) \(2 \vec{a} \cdot \vec{b}+2 \vec{b} \cdot \vec{c}+2 \vec{c} \cdot \vec{a}=2 \vec{a} \cdot \vec{b}-2 \vec{b} \cdot \vec{c}-2 \vec{c} \cdot \vec{a}\) \(4 \vec{a} \cdot \vec{c}=0\) \(B\) is incorrect…
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