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

Answers (1)

It is given that the line is passing through A (1, 2, 3) and is parallel to the vector \vec{b}=3\widehat{i}+2\widehat{j}-2\widehat{k}

We can easily find the equation of the line which passes through the point A and is parallel to the vector \vec{b} by the known relation;

\vec{r} = \vec{a} +\lambda\vec{b}, where \lambda is a constant.

So, we have now,

\\\mathrm{\Rightarrow \vec{r} = \widehat{i}+2\widehat{j}+3\widehat{k} + \lambda(3\widehat{i}+2\widehat{j}-2\widehat{k})} 

Thus the required equation of the line.

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