MathematicsMedium202×since 2002Q5781Let a⃗=2i^+j^+k^\vec{a}=2 \hat{i}+\hat{j}+\hat{k}a=2i^+j^+k^, and b⃗\vec{b}b and c⃗\vec{c}c be two nonzero vectors such that ∣a⃗+b⃗+c⃗∣=∣a⃗+b⃗−c⃗∣|\vec{a}+\vec{b}+\vec{c}|=|\vec{a}+\vec{b}-\vec{c}|∣a+b+c∣=∣a+b−c∣ and b⃗⋅c⃗=0\vec{b} \cdot \vec{c}=0b⋅c=0. Consider the following two statements: (A) ∣a⃗+λc⃗∣≥∣a⃗∣|\vec{a}+\lambda \vec{c}| \geq|\vec{a}|∣a+λc∣≥∣a∣ for all λ∈R\lambda \in \mathbb{R}λ∈R. (B) a⃗\vec{a}a and c⃗\vec{c}c are always parallel. Then,Aonly (B) is correctBboth (A) and (B) are correctConly (A) is correctDneither (A) nor (B) is correctCheck answerSkip