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

Find the angle between the line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and the plane vecr.(2hati-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 angles between the line vecr=-hati+hatj+2hatk+lambda(3hati+2hatj+4hatk) and the plane vecr.(2hati+hatj-3hatk)+4=0

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

The angle between the lines vecr=(5hati-hatj-4hatk)+lambda(2hati-hatj+hatk) and the plane vecr.(3hati-4hatj-hatk)+5=0 is sin^-1(5/2sqrt91) .

Find the distance of the point with position vector -hati-5hatj-10hatk from the point of intersection of the line vecr=(2hati-hatj+2hatk)+lambda(3hati+4hatj+12hatk) and the plane vecr*(hati-hatj+hatk)=5 .

Find the point of intersection of the line : vecr=(hati+2hatj+3hatk)+lambda(2hati+hatj+2hatk) and the plane vecr*(2hati-6hatj+3hatk)+5=0 .

Find the angle between the lines vecr=2hati+3hatj-4hatk+lambda(2hati+1hatj+2hatk) and vecr=2hati-5hatk+mu(6hati+3hatj+2hatk)

Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) lies in the plane vecr*(3hati+hatj-hatk)+2=0 .