Find the distance of the point (2, 3, -1) from the point of intersection of the line `vecr=3hati+hatj-2hatk+lambda(3hati+6hatj+2hatk)` and the plane `vecr.(2hati-hatj+hatk)`=3.

Find the distance of the point (-1 , -5 , -10) from the point of intersection of the line vecr=2hati-hatj+2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr.(hati-hatj+hatk) =5.

Find the distance of the point (2,12,5) from the point of intersection of the line: vecr=2hati-4hatj+2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr*(hati-2hatj+hatk)=0 .

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

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

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

Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr*(hati+2hatj-hatk)=3 .

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