Question

The vector equation of the line passing through the points (3, 2, 1) and (1, 3, 1) is ______.

पर्याय

• `bar"r" = 3hat"i" + 2hat"j" + hat"k" + lambda(-2hat"i" + hat"j" + hat"k")`

• `bar"r" = 3hat"i" + 2hat"j" + hat"k" + lambda(-2hat"i" + hat"j" - hat"k")`

• `bar"r" = 3hat"i" + 2hat"j" + hat"k" + lambda(-2hat"i" + hat"j")`

• `bar"r" = 3hat"i" + 2hat"j" + hat"k" + lambda(2hat"i" + hat"j")`

Answer 1

The vector equation of the line passing through the points (3, 2, 1) and (1, 3, 1) is `bar"r" = 3hat"i" + 2hat"j" + hat"k" + lambda(-2hat"i" + hat"j")`.

Explanation:

Let `bar"a"` and `bar"b"` be the position vectors of the points.

∴ `bar"a" = 3hat"i" + 2hat"j" + hat"k"` an `bar"b" = hat"i" + 3hat"j" + hat"k"`

∴ `bar"b" - bar"a" = hat"i" + 3hat"j" + hat"k" - 3hat"i" - 2hat"j" - hat"k" = -2hat"i" + hat"j"`

The vector equation of line is given by

`bar"r" = bar"a" + lambda(bar"b" - bar"a")`

⇒ `bar"r" = 3hat"i"  + 2hat"j" + hat"k" + lambda(-2hat"i" + hat"j")`