Find the vector equation of the line which passes through the point $(3, 4, 5)$ and is parallel to the vector $2^i + 2^j - 3^k .$

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Solution

The vector equation of a line which passes through the point $\to a$ and parallel to the vector $\to b$ is given as
$\to r = \to a + λ \to b,$ where $λ$ is a scalar.
$Here, \to a = 3^i + 4^j + 5^k and \to b = 2^i + 2^j - 3^k$
So, Required equation is $\to r = 3^i + 4^j + 5^k + λ (2^i + 2^j - 3^k)$

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