​ 1.State the condition for the line bar r = bar a + λ bar b is parallel to the plane bar (r.n) = d. ​

Question

1.State the condition for the line \(\bar{r}\) = \(\bar a\) + λ \(\bar b\) is parallel to the plane \(\bar{r}\).\(\bar n\) = d. 

2. Show that the line \(\bar{r}\) = i + j + λ(2i + j + 4k) is parallel to the plane \(\bar{r}\). (-2i + k) = 5. 

3. Find the distance between the line and The Plane in (ii).

Answer 1

1. The line \(\bar r\) = \(\bar a\) + λ \(\bar b\) is parallel to the plane \(\bar r.\bar n\) = d, if the normal of the plane is perpendicular to the line.

∴ \(\bar b.\bar n = 0.\)

2. Given,

The line \(\bar r\) = i + j + λ(2i + j + 4k) is parallel to the plane \(\bar r\). (-2i + 4k) = 5 ⇒ -2x + 4y = 5.

3. Distance = Distance between – 2x + 4y = 5 and point (1, 1, 0) on the line