Let the vectors 2-a-b-a-2b-c-b-ck- 1-b-2b-bk- and 2-b-2b-1-bk- a-b-c -be co-planar- Then which of the following is true -

For coplanarity S.T.P. of given vectors shall vanish 2+a+b amp;a+2b+c nbsp; amp; (b+c) nbsp; 1+b amp;2b nbsp; amp; b nbsp; 2+b amp;2 ...

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Unit Vectors

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Question

Let the vectors $(2 + a + b)^i + (a + 2 b + c)^j - (b + c)^k,$ $(1 + b)^i + 2 b^j - b^k$ and $(2 + b)^i + 2 b^j + (1 - b)^k,$ $a, b, c \in R$
be co-planar. Then which of the following is true ?

3 c = a + b

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2 b = a + c

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2 a = b + c

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a = b + 2 c

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a^i + b^j + c^k; b^i + c^j + a^k

c^i + a^j + b^k

\to α = a^i + b^j + c^k, \to β = b^i + c^j + a^k

\to γ = c^i + a^j + b^k

a \neq b \neq c

\to v =^i +^j +^k

\to v

_{1} = a^i + b^j + c^k

_{2} = b^i + c^j + a^k

_{3} = c^i + a^j + b^k

_{1},_{2}

_{3}

\to α = a^i + b^j + c^k, \to β = b^i + c^j + a^k

\to γ = c^i + a^j + b^k

\to α \neq \to β \neq \to γ

\to r =^i +^j +^k,

\to r

m

P_{1}

P_{2}

{\to r}_{1} = a^i + b^j + c^k; {\to r}_{2} = c^i + a^j + b^k

\to F = b^i + c^j + a^k

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