Find the equation of a line, which is parallel to $straight i with hat on top plus straight j with hat on top plus straight k with hat on top$ and passes through (2, 3, 1).

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

We know that the equation of a straight line passing through a fixed point with position vector

straight a with rightwards arrow on top

and parallel to the vector

straight m with rightwards arrow on top space is space straight r with rightwards arrow on top space equals space straight a with rightwards arrow on top plus straight lambda straight m with rightwards arrow on top

where λ is a parameter.
Here

straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus space 3 straight j with hat on top space plus space straight k with hat on top space and space straight m with rightwards arrow on top space equals space straight i with hat on top plus straight j with hat on top plus straight k with hat on top

∴ from (1), the vector equation of line is

straight r with rightwards arrow on top space equals space left parenthesis 2 straight i with hat on top space plus space 3 space straight j with hat on top space plus space straight k with hat on top right parenthesis space plus space straight lambda space left parenthesis straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top right parenthesis

For Daily Free Study Material Join wiredfaculty