A line passes through the point with position vector `2 hat i-3 hat j+4 hat k` and is in the direction of `3 hat i+4 hat j-5 hat kdot` Find equations of the line in vector and Cartesian form.

Explanation

Since the line passes through `2 hat{i}-3 hat{j}+4 hat{k}` and has direction of `3 hat{i}+4 hat{j}-5 hat{k}`,


its vector equation is


`vec{r}=hat{a}+lambda hat{b}`


` Rightarrow vec{r}=2 hat{i}-3 hat{j}+4 hat{k}+lambda(3 hat{i}+4 hat{j}-5 hat{k})`, where `lambda` is a рагаmeter.


Cartesian equation ` => frac{x-2}{3}=frac{y+3}{4}=frac{z-4}{-5}`