Let a=2 i+ j+ k, and b, c be non-zero vectors such that | a+ b+ c|=| a+ b- c| and b c=0.

Question

Accepted Answer

Expanding $|\vec a+\vec b+\vec c|^2=|\vec a+\vec b-\vec c|^2$: $4(\vec a+\vec b)\cdot\vec c=0 \Rightarrow \vec a\cdot\vec c+\vec b\cdot\vec c=0 \Rightarrow \vec a\cdot\vec c=0$ (using $\vec b\cdot\vec c=0$).

So $\vec a\perp\vec c$ always --- hence (B) is false (perpendicular, not parallel, unless $\vec c=\vec 0$, excluded).

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