The non-parametric vector equation of a plane passing through the points whose position vectors are $\to a$ and $\to b$ ; and parallel to $\to v$ , is

[\begin{matrix} \to r - \to a & \to b - \to a & \to v \end{matrix}] = 0

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[\begin{matrix} \to r & \to b - \to a & \to v \end{matrix}] = 0

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[\begin{matrix} \to a & \to b & \to v \end{matrix}] = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

[\begin{matrix} \to r & \to a & \to b \end{matrix}] = 0

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Solution

The correct option is A $[\begin{matrix} \to r - \to a & \to b - \to a & \to v \end{matrix}] = 0$
Let $\to r$ be any point in the required plane
So normal vector to the plane is given by $(\to r - \to a) \times (\to b - \to a)$
Also since plane is parallel to $\to v$
So dot product of above vector will be zero
$(\to r - \to a) \times (\to b - \to a) \cdot v = 0$
$\Rightarrow [\to r - \to a \to b - \to a \to v] = 0$

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The non-parametric vector equation of a plane passing through the points whose position vectors are →a and →b; and parallel to →v, is

The non-parametric vector equation of a plane passing through the points whose position vectors are $\to a$ and $\to b$ ; and parallel to $\to v$ , is