Let α ∈ R and the three vectors a → = α i ^ + j ^ + 3 k ^ , b → = 2 i ^ + j ^ - α k ^ and c → = α i ^ - 2 j ^ + 3 k ^ . Then the set S = { α : a → , b → and c → are coplanar}

If a → , b → and c → are coplanar then, α 1 3 2 1 - α α - 2 3 = 0 ⇒ 3 α 2 + 18 = 0 ⇒ α ∈ ϕ

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Mathematics - Vector Question with Solution | TestHub

MathematicsVectorGeneral definitions, Angle between vectors, Section formula, Geometrical resultsEasy2 minPYQ_2019

MathematicsEasysingle choice

Let $α \in R$ and the three vectors $\vec{a} = α \hat{i} + \hat{j} + 3 \hat{k}, \vec{b} = 2 \hat{i} + \hat{j} - α \hat{k}$ and $\vec{c} = α \hat{i} - 2 \hat{j} + 3 \hat{k} .$ Then the set S = { $α : \vec{a}, \vec{b}$ and $\vec{c}$ are coplanar}

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Answer:

Solution:

If $\vec{a}, \vec{b} and \vec{c}$ are coplanar then,
$|\begin{matrix} α & 1 & 3 \\ 2 & 1 & - α \\ α & - 2 & 3 \end{matrix}| = 0$
$\Rightarrow 3 α^{2} + 18 = 0$
$\Rightarrow α \in ϕ$

Stream:JEESubject:MathematicsTopic:VectorSubtopic:General definitions, Angle between vectors, Section formula, Geometrical results

⏱ 2mℹ️ Source: PYQ_2019

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