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

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Solution

Given that, line is passing through $(1, 2, 3)$ and parallel to vector $3^i + 2^j - 2^k$
$∴$ Vector equation of line $= ¯ r = (^i + 2^j + 3^k) + t (3^i + 2^j - 2^k)$
Cartesian equation is $\frac{x - 1}{3} = \frac{y - 2}{2} = \frac{z - 3}{- 2}$

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