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

Let r⃗≠ 0.Then r⃗.a⃗=r⃗.b⃗=r⃗.c⃗=0 ⇒a⃗, b⃗,c⃗ are coplanar, which is a contradiction. Therefore,r⃗=0⃗ ...

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Applications of Dot Product

If r⃗.a⃗=r⃗.b...

Question

If $\to r . \to a = \to r . \to b = \to r . \to c = 0$ where $\to a, \to b, \to c$ are non – coplanar, then

\to r ⊥ (\to c \times \to a)

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\to r ⊥ (\to a \times \to a)

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\to r ⊥ (\to b \times \to c)

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\to r = \to 0

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Solution

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