Find the vector equation of the passing through the point $2 i + 3 j + k$ and parallel to the vector $4 i - 2 j + 3 k$ .

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Solution

The line passes through the point,
Say $\to a = 2^i + 3^j +^k$
And parallel to the line,
say $\to b = 4^i - 2^j + 3^k$
The vector equation of the line passing through apoint and parallel to the given line is,
$\to r = \to a + λ \to b$
Substituting the values, we get,
$\to r = (2^i + 3^j +^k) + λ (4^i - 2^j + 3^k)$
$\to r = (2 + 4 λ)^i + (3 - 2 λ)^j + (1 + 3 λ)^k$

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