If r¯.a¯=r¯.b¯=r¯.c¯=0, where a¯, b¯, c¯ are non coplanar then

r·a=r·b=r·c=0 ⇒ r ⊥ a, r ⊥ b, r ⊥ c ⇒ r || a×b or r || b×c or r || c×abut a, b, c are coplanor ⇒ r=0

If r¯.a¯=r¯.b¯=r¯.c¯=0, where a¯, b¯, c¯ are non coplanar then

r·a=r·b=r·c=0 ⇒ r ⊥ a, r ⊥ b, r ⊥ c ⇒ r || a×b or r || b×c or r || c×abut a, b, c are coplanor ⇒ r=0

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$If \bar{r} . \bar{a} = \bar{r} . \bar{b} = \bar{r} . \bar{c} = 0, where \bar{a}, \bar{b}, \bar{c} are non coplanar then$

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$\bar{r} = \bar{a}$

$\bar{r} = \bar{b}$

$\bar{r} = \bar{0}$

$\bar{r} = \bar{c}$

answer is C.

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$\begin{array}{rcl} r \cdot a & = & r \cdot b = r \cdot c = 0 \\ \Rightarrow & r ⊥ a, r ⊥ b, r ⊥ c \Rightarrow r | | a \times b \\ or r | | b \times c or r | | c \times a \end{array}$

but $a, b, c$ are coplanor $\Rightarrow r = 0$

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If r¯.a¯=r¯.b¯=r¯.c¯=0, where a¯, b¯, c¯ are non coplanar then

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$If \bar{r} . \bar{a} = \bar{r} . \bar{b} = \bar{r} . \bar{c} = 0, where \bar{a}, \bar{b}, \bar{c} are non coplanar then$