If a- b- c are non coplanar vectors and - is a real number- then the vectors a-2b-3c- -b- 4c and 2- -1c are non coplanar for-

Condition for the given three vectors to be coplanar is: 1 amp;2 amp;3 0 amp;λ amp; 4 0 amp;0 amp;2λ 1 =0 On solving, we have λ=0, 12 Hence, given ...

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Standard XII

Mathematics

Equal Vectors

If a, b, c ar...

Question

If $\to a, \to b, \to c$ are non coplanar vectors and $λ$ is a real number, then the vectors $\to a + 2 \to b + 3 \to c, λ \to b + 4 \to c$ and $(2 λ - 1) \to c$ are non coplanar for:

all values of

λ

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all except one values of

λ

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all except two values of

λ

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no values of

λ

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Solution

The correct option is C all except two values of $λ$
Condition for the given three vectors to be coplanar is:
$∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 3 0 & λ & 4 0 & 0 & 2 λ - 1 \end{matrix} ∣ ∣ ∣ ∣ = 0$
On solving, we have $λ = 0, \frac{1}{2}$
Hence, given vectors will be non coplanar for all real values of $λ$ except $0 and \frac{1}{2}$

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Equal Vectors

Standard XII Mathematics

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If →a,→b,→c are non coplanar vectors and λ is a real number, then the vectors →a+2→b+3→c,λ→b+4→c and (2λ−1)→c are non coplanar for:

The correct option is C all except two values of λCondition for the given three vectors to be coplanar is: ∣∣ ∣∣1230λ4002λ−1∣∣ ∣∣=0 On solving, we have λ=0,12 Hence, given vectors will be non coplanar for all real values of λ except 0 and 12

If $\to a, \to b, \to c$ are non coplanar vectors and $λ$ is a real number, then the vectors $\to a + 2 \to b + 3 \to c, λ \to b + 4 \to c$ and $(2 λ - 1) \to c$ are non coplanar for: