Find the angle between the line joing (3,-4,-2) and(12, 2, 0) and the plane `vecr*(hati+hatj+hatk)=4`

Find the angle between the line : vecr=(hati-hatj+hatk)+lambda(2hati-hatj+3hatk) and the plane vecr*(2hati+hatj-hatk)=4 . Also find whether the line is parallel to the plane or not.

Find the angle between the line vecr=(hati+hatj+hatk)+lambda(2hati-hatj-hatk) and the plane vecr.(hati+hatj-2hatk) =3.

Find the angle between the line vecr=(hati-hatj+3hatk)+lambda(2hati-hatj+hatk) and the plane vecr.(hati+hatj+2hatk) =4.

Find the angle between the line : (2hati+3hatj+4hatk)+lambda(2hati+3hatj+4hatk) and the plane : vecr*(hati+hatj+hatk)=5 .

Find the angle between the planes : vecr*(2hati+2hatj-3hatk)=5 and vecr*(3hati-3hatj+5hatk)=3

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes vecr.(hati-hatj+2hatk)=5 and vecr.(3hati+hatj+hatk)=6.

Find the angle between the line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and the plane vecr.(2hati-hatj+hatk)=4 .

Find the vector equation of the line passing through (1, 2, 3) and parallel to each of the planes vecr = (hati-hatj+2 hatk)= 5" and "vecr *(3hati- hatj+hatk)= 6 . Also find the point of intersection of the line thus obtained with the plane vecr * (2hati-hatj+hatk)= 4 .

Find the acute angle between the planes vecr.(hati+2hatj-hatk)=3 and vecr.(2hati-hatj+2hatk)=2 .

Find the angle between the planes whose vector equations are vecr cdot(2hati+2hatj - 3hatk) = 5 and vecr cdot(3hati-3hatj+5hatk) = 3