Question

Find the vector equation of the line passing through the point 2 3 i j k   and parallel

to the vector 4 2 3 i j k   .​

Answer 1

SOLUTION

TO DETERMINE

The vector equation of the line passing through the point $2 \hat{i} + 3 \hat{j} + \hat{k}$ and parallel to the vector $4 \hat{i} + 2 \hat{j} + 3 \hat{k}$

FORMULA TO BE IMPLEMENTED

The vector equation of a line passing through the point $\vec{a}$ and parallel to the vector $\vec{b}$ is

$\vec{r} = \vec{a} + t \vec{b}$

Where t is a real parameter

EVALUATION

Here the given point is $2 \hat{i} + 3 \hat{j} + \hat{k}$

Also the given vector is $4\hat{i} + 2 \hat{j} + 3 \hat{k}$

Hence the required vector equation of the line is

$\vec{r} = (2 \hat{i} + 3 \hat{j} + \hat{k}) + t(4 \hat{i} + 2 \hat{j} + 3\hat{k})$

Where t is a real parameter

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