The vectors x- - x - 1 - - x - 2k- x - 3- - x - 4- - x - 5k- and x - 6- - x - 7- - x - 8 k- are coplanar if x is equal to

The correct options are A 1 B 3 C 4 D 0 xi^+(x+1)j^+(x+2)k^,(x+3)i^+(x+4)j^+(x+5)k^xi^+(x+1)j^+(x+2)k^,(x+3)i^+(x+4)j^+(x+5)k^ for all x ...

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Condition for Coplanarity of Four Points

The vectors ...

Question

The vectors $x^i + (x + 1)^j + (x + 2)^k$ , $(x + 3)^i + (x + 4)^j + (x + 5)^k$ and $(x - 6)^i + (x + 7)^j + (x + 8)^k$ are coplanar if $x$ is equal to

1

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- 3

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4

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0

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Solution

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\to a = x^i + (x + 1)^j + (x + 2)^k, \to b = (x + 3)^i + (x + 4)^j + (x + 5)^k

\to c = (x + 6)^i + (x + 7)^j + (x + 8)^k

\to a = x^i + (x + 1)^j + (x + 2)^k, \to b = (x + 3)^i + (x + 4)^j + (x + 5)^k

\to c = (x + 6)^i + (x + 7)^j + (x + 8)^k

\to a = x^i + (x + 1)^j + (x + 2)^k, \to b = (x + 3)^i + (x + 4)^j + (x + 5)^k

\to c = (x + 6)^i + (x + 7)^j + (x + 8)^k

a = 2^i -^j +^k, b = x^i + 2^j - 3^k

c = 3^i - 4^j + 5^k

\to a =^i +^j +^k, \to b =^i -^j + 2^k, \to c = x^i + (x - 2)^j -^k

x =

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