If r-a- - r-b- - r-c- - 0- where a- b- and c- are non-coplanar- then

The correct option is D r⃗ = 0⃗ Let r⃗≠ #160;0⃗ , then r⃗· #160;a⃗ = #160;r⃗· #160;b⃗ = #160;r⃗· #160;c⃗ = 0 Hence, a⃗ , #160 ...

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Applications of Dot Product

If r⃗·a⃗ = ...

Question

If $\to r \cdot \to a = \to r \cdot \to b = \to r \cdot \to c = 0$ , where $\to a, \to b$ and $\to c$ are non-coplanar, then

\to r ⊥ (\to c \times \to a)

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\to r ⊥ (\to a \times \to b)

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\to r ⊥ (\to b \times \to c)

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\to r = \to 0

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Let $\to r$ be the only point of intersection of the planes $\to r . \to a = P_{1}, \to r . \to b = P_{2}, \to r . \to c = P_{3}$ then

\to a, \to b, \to c

\to r

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b) =

\to r . \to a = \to r . \to b = \to r . \to c = 0

\to a, \to b, \to c

\to a, \to b, \to c

\to r

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b)

\to a, \to b

\to c

[\to a + \to b, \to b + \to c, \to c + \to a] = 2 [\to a \to b \to c]

\to a + \to b, \to b + \to c, \to c + \to a

\to a, \to b, \to c

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