Find the equation of the plane which passes through the points $2 i + 4 j + 2 k$ and $2 i + 3 j + 5 k$ and parallel to the vector $3 i - 2 j + k$ .

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Solution

Equation of plane:
$\to r = (1 - s) \to a + s \to b + t \to c$
$\begin{matrix} \to a = 2^i + 4^j + 2^k \to b = 2^i + 3^j + 5^k \to c = 3^i - 2^j +^k \to r = (1 - s) (2^i + 4^j + 2^k) + s (2^i + 3^j + 5^k) + t (3^i - 2^j +^k) \to r = (3 t + 2)^i + (4 - s - 2 t)^j + (2 + 3 s + t)^k \end{matrix}$

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