Question
Find the vector equation of line passing through the point having position vector
$5 \hat{i}+4 \hat{j}+3 \hat{k}$ and having direction ratios $-3,4,2$.
$5 \hat{i}+4 \hat{j}+3 \hat{k}$ and having direction ratios $-3,4,2$.
Let $\bar{b}$ be the vector parallel to the line having direction ratios $-3,4,2$
Then, $\bar{b}=-3 \hat{i}+4 \hat{j}+2 \hat{k}$
The vector equation of the line passing through $\mathrm{A}(\bar{a})$ and parallel to $\bar{b}$ is $\bar{r}=\bar{a}+\lambda \bar{b}$,
where λ is a scalar. ∴ the required vector equation of the line is
$\bar{r}=5 \hat{i}+4 \hat{j}+3 \hat{k}+\lambda(-3 \hat{i}+4 \hat{j}+2 \hat{k})$.
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$\frac{d^2 y}{d t^2}+\left(\frac{d y}{d t}\right)^2+7 x+5=0$