Question

The Cartesian equation of the line passing through the point (1, −3, 2) and parallel to the line:

`overset->r = (2 + lambda)hat i + lambda hat j + (2 lambda - 1) hat k` is:

Options

• `(x -1)/2 = (y + 3)/0 = (z - 2)/-1`

• `(x +1)/1 = (y - 3)/1 = (z + 2)/2`

• `(x +1)/2 = (y - 3)/0 = (z + 2)/-1`

• `(x -1)/1 = (y + 3)/1 = (z - 2)/2`

Answer 1

`bb((x -1)/1 = (y + 3)/1 = (z - 2)/2)`

Explanation:

Given line is  `overset->r = (2 + lambda)hat i + lambda hat j + (2 lambda - 1) hat k`

`overset->r = (2 hat i - hat k) + lambda (hat i + hat j + 2 hat k)`

which is of the form  `overset->r = a + lambda overset->b`

∴ Required line is  `(x - 1)/1 = (y + 3)/1 = (z - 2)/2`

[As lines passes through (1, −3, 2) and having Direction cosines (1, 1, 2)]