Find the equation of the line which passes through the point $(1, 2, 3)$ and is parallel to the vector $(3^i + 2^j - 2^k$ .

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Solution

It is given that the line passes through the point $A (1, 2, 3)$ .
Therefore, the position vector through $A$ is $\to a =^i + 2^j + 3^k$
$\to b = 3^i + 2^j - 2^k$
It is known that the line which passes through point $A$ and parallel to $\to b$ is given by $\to r = \to a + λ \to b$ , where $λ$ is a constant.
$\Rightarrow$ $\to r =^i + 2^j + 3^k + λ (3^i + 2^j - 2^k)$
This is the required equation of the line.

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