Prove that points A- B- C having positions vectors a- -b- -c- are collinear- if -b-c- -c-a- -a-b-0-

If A,B,C are collinear, A̅B̅ and B̅C̅ are parallel. ⇒A̅B̅×B̅C̅=0 (b̅ a̅)× (c̅ b̅)=0 b̅×c̅ b̅×b̅ a̅×c̅+a̅×b̅=0 But, b̅×b̅=0 b̅ ...

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Dot Product

Prove that po...

Question

Prove that points $A, B, C$ having positions vectors $\to a, \to b, \to c$ are collinear, if $[\to b \times \to c + \to c \times \to a + \to a \times \to b] = \to 0$

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\to a, \to b, \to c

\to a + \to b + \to c = \to 0

(\to a, \to b) = \frac{π}{3}

| \to a \times \to b | + | \to b \times \to c | + | \to c \times \to a | =

\to a, \to b, \to c

\to a + \to b + \to c = \to 0

(\to a, \to b) = \frac{π}{3}

∣ ∣ \to a \times \to b ∣ ∣ + ∣ ∣ \to b \times \to c ∣ ∣ + | \to c \times \to a | =

\to a, \to b, \to c

\to a \times \to b = \to c, \to b \times \to c = \to a, \to c \times \to a = \to b

| \to a | = | \to b | = | \to c |

\to a, \to b, \to c

A, B, C

Δ A B C

\to r

P

(| \to b - \to c | + | \to c - \to a | + | \to a - \to b |) \to r = | \to b - \to c | \to a + | \to c - \to a | \to b + ∣ ∣ \to a - \to b ∣ ∣ \to c

P

\to a, \to b, \to c

\to a \times \to b = \to b \times \to c = \to c \times \to a

\to a + \to b + \to c =

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