Question

The equation of the line passing through (1, 2, 3) and perpendicular to the lines `x - 1 = (y + 2)/2 = (z + 4)/4` and `(x - 1)/2 = (y - 2)/2` = z + 3 is ______.

विकल्प

• `x - 1 = (y - 2)/2 = (z - 3)/4`

• `(x - 1)/4 = (2 - y)/5 = (z - 3)/2`

• `(x - 1)/6 = (y - 2)/7 = (z - 3)/2`

• `(x - 1)/6 = (2 - y)/7 = (z - 3)/2`

Answer 1

`(x - 1)/6 = (2 - y)/7 = (z - 3)/2`

Explanation:

Given line,

`(x - 1)/1 = (y + 2)/2 = (z + 4)/4`

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

The direction ratio of given line are

`(hat"i" + 2hat"j" + 4hat"k") and 2hat"i" + 2hat"j" + 1 hat"k"` respectively.

Direction ratio of line perpendicular to both the given line is `(hat"i" + 2hat"j" + 4hat"k") xx (2hat"i" + 2hat"j" + 1 hat"k")`

`= |(hat"i", hat"j", hat"k"),(1,2,4),(2,2,1)|`

`= - 6hat"i" + 7hat"j" - 2hat"k"`

Equation of line passing through (1, 2, 3) and whose parallel vector `- 6hat"i" + 7hat"j" - 2hat"k"` is

or `(x - 1)/(- 6) = (y - 2)/7 = (z - 3)/(-2)`

`=> (x - 1)/6 = (2 - y)/7 = (z - 3)/2`