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(A) The equation of a line passing through a point with position vector $\vec{a}$ and parallel to a vector $\vec{b}$ is given by $\vec{r} = \vec{a} +

Vedclass · Accepted Answer

$\vec{r} = \hat{i} + 2 \hat{j} + 3 \hat{k} + \lambda(3 \hat{i} + 2 \hat{j} - 2 \hat{k})$

Vedclass · Answer

(A) The equation of a line passing through a point with position vector $\vec{a}$ and parallel to a vector $\vec{b}$ is given by $\vec{r} = \vec{a} + \lambda \vec{b}$.Given the point $(1, 2, 3)$,the position vector is $\vec{a} = \hat{i} + 2 \hat{j} + 3 \hat{k}$.Given the parallel vector $\vec{b} = 3 \hat{i} + 2 \hat{j} - 2 \hat{k}$.Substituting these into the formula,we get $\vec{r} = \hat{i} + 2 \hat{j} + 3 \hat{k} + \lambda(3 \hat{i} + 2 \hat{j} - 2 \hat{k})$.

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

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