If the four points, whose position vectors are $$3\widehat i - 4\widehat j + 2\widehat k,\widehat i + 2\widehat j - \widehat k, - 2\widehat i - \widehat j + 3\widehat k$$ and $5\widehat i - 2\alpha \widehat j + 4\widehat k$ are coplanar, then $\alpha$ is equal to :
Solution
Let $\mathrm{A}:(3,-4,2) \quad \mathrm{C}:(-2,-1,3)$<br/><br/>
$\text { B : }(1,2,-1) \quad \text { D: }(5,-2 \alpha, 4)$<br/><br/>
A, B, C, D are coplanar points, then<br/><br/>
$$
\begin{aligned}
& \Rightarrow\left|\begin{array}{ccc}
1-3 & 2+4 & -1-2 \\
-2-3 & -1+4 & 3-2 \\
5-3 & -2 \alpha+4 & 4-2
\end{array}\right|=0 \\\\
& \Rightarrow \alpha=\frac{73}{17}
\end{aligned}
$$
About this question
Subject: Mathematics · Chapter: Vector Algebra · Topic: Types of Vectors
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