Find the image of the point `hati+3hatj+4hatk` in the plane `vecr.(2hati-hatj+hatk)+3=0`.

Find the distance of the point whose position vector is 2hati+hatj-hatk from the plane vecr.(hati-2hatj+4hatk)=9 .

Find the distane of the point P(hati+hatj+hatk) from the plane through the points A(2hati+hatj+hatk) , B(hati+2hatj+hatk) and C(hati+hatj+2hatk)

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 plane passing through the intersection of the planes vecr.(hati+hatj+hatk) =6 and vecr.(2hati+3hatj+4hatk)=-5 and point (1,1,1)

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 equations of the plane through the intersection of the planes vecr.(hati-1hatj)=-6 and vecr.(3hati+3hatj-4hatk)=0 , whose perpendicular distance form the origin is unity.

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

True or false The line vecr=2hati-3hatj+hatk+t(hati-hatj+2hatk) lies in the plane vecr.(3hati+hatj-hatk)-2=0 .

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 .