If a - b - c are non-coplanar vectors such that x-y-3 a - 2x-y-2 b - 2x-y- c holds true for some x and y then - is

The correct option is D 10 3 Since a , b , c #10; are non coplanar vectors x+y 3=0, 2x y+2=0 and #10; 2x+y+λ=0 #160; 1 ...

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Byju's Answer

Standard XII

Mathematics

Condition for Coplanarity of Four Points

If a , b , ...

Question

If $\to a, \to b, \to c$ are non-coplanar vectors such that
$(x + y - 3) \to a + (2 x - y + 2) \to b + (2 x + y + λ) \to c$ holds true for some $x$ and $y$ then $λ$ is

\frac{7}{3}

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2

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\frac{- 10}{3}

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\frac{5}{3}

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Solution

The correct option is D $\frac{- 10}{3}$
Since $\to a, \to b, \to c$ are non-coplanar vectors $x + y - 3 = 0, 2 x - y + 2 = 0$ and $2 x + y + λ = 0$
$∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & - 3 2 & - 1 & 2 2 & 1 & λ \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow λ = \frac{- 10}{3}$

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Similar questions

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∣ ∣ \to a ∣ ∣ = 3, ∣ ∣ ∣ \to b ∣ ∣ ∣ = 5, ∣ ∣ \to c ∣ ∣ = 7

such that

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Reason:

{(\to x + \to y)}^{2} = {∣ ∣ \to x ∣ ∣}^{2} + {∣ ∣ \to y ∣ ∣}^{2} + 2 (\to x \cdot \to y)

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and

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and

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If →a,→b,→c are non-coplanar vectors such that(x+y−3)→a+(2x−y+2)→b+(2x+y+λ)→c holds true for some x and y then λ is

The correct option is D −103Since →a,→b,→c are non-coplanar vectors x+y−3=0,2x−y+2=0 and 2x+y+λ=0 ∣∣ ∣∣11−32−1221λ∣∣ ∣∣=0⇒λ=−103

If $\to a, \to b, \to c$ are non-coplanar vectors such that
$(x + y - 3) \to a + (2 x - y + 2) \to b + (2 x + y + λ) \to c$ holds true for some $x$ and $y$ then $λ$ is

The correct option is D $\frac{- 10}{3}$
Since $\to a, \to b, \to c$ are non-coplanar vectors $x + y - 3 = 0, 2 x - y + 2 = 0$ and $2 x + y + λ = 0$
$∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & - 3 2 & - 1 & 2 2 & 1 & λ \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow λ = \frac{- 10}{3}$