MCQ
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
- Aonly $(B)$ is correct
- Bneither $(A)$ nor $(B)$ is correct
- ✓only $(A)$ is correct
- Dboth $(A)$ and $(B)$ are correct.