Question

The line l has equation r=(1 2 -1) + lamda(2 1 3). The plane has equation r.(2 -1 -1)=6 (i) show that l is parallel to p Can someone please solve this question?

Answer 1

See explanation.

Explanation:

The direction vector of the line is `[2,1,3]`. That vector is parallel to the line.

The normal vector to the plane is `[2, -1, -1]`. That vector, as the name implies, is normal to the plane.

Calculating the dot product of the two vectors gives:

`[2,1,3] cdot [2, -1, -1] = 4-1-3=0`

Since the dot product is 0 we know the vectors are orthogonal.

Since both the plane and the line are orthogonal to the vector `[2, -1, -1]` they are parallel to each other.