Question

A line passes through \[(5,2,-4)\] and is parallel to \[3\hat{i}+2\hat{j}-8\hat{k}\]. Which is its vector equation?

Options

• \[\vec{r}=(3\hat{i}+2\hat{j}-8\hat{k})+\lambda(5\hat{i}+2\hat{j}-4\hat{k})\]

• \[\vec{r}=(5\hat{i}+2\hat{j}+4\hat{k})+\lambda(3\hat{i}+2\hat{j}-8\hat{k})\]

• \[\vec{r}=(5\hat{i}+2\hat{j}-4\hat{k})+\lambda(3\hat{i}+2\hat{j}-8\hat{k})\]

• \[\vec{r}=(5\hat{i}+2\hat{j}-4\hat{k})+\lambda(3\hat{i}-2\hat{j}-8\hat{k})\]

Answer 1

The point gives \[\vec{a}=5\hat{i}+2\hat{j}-4\hat{k}\]. The vector parallel to the line is \[\vec{b}=3\hat{i}+2\hat{j}-8\hat{k}\], so these are substituted in \[\vec{r}=\vec{a}+\lambda\vec{b}\].