Position vectors of A- B- C are given by a- b- c- where a-b-b-c-c-a-0- If A-C-2-3-6k- find B-C- if BC -14-

Position vector of A, B,C are a ,b ,c respectively Given #160; [ a × b + b × c + c × a =0; A,B,C are collinea ...

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Applications of Cross Product

Position vect...

Question

Position vectors of A, B, C are given by $\to a, \to b, \to c$ where $\to a \times \to b + \to b \times \to c + \to c \times \to a = 0$ . If $\to A C = 2^i - 3^j + 6^k$ find $\to B C$ if BC $= 14$ .

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

\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

A, B, C

Δ A B C

\to r

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(| \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

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[\to a \to b \to c] = \to k

k \neq 0

[(\to b \times \to c) \times (\to c \times \to a) (\to c \times \to a) \times (\to a \times \to b) (\to a \times \to b) \times (\to b \times \to c)] =

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\to a, \to b, \to c

[\to b \times \to c + \to c \times \to a + \to a \times \to b] = \to 0

\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 |

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