If `A(2bar i-bar j-3bar k), B(4bari+barj-bark) ,C(bar i -3bar j+2bar k),D(bar i-bar j-2bar k)` then the vector equation of plane parallel to `bar(ABC)` and passing through centriod of the tetrahedron ABCD is

If (2bar(i)-bar(j)-3bar(k)),B(4bar(i)+bar(j)-bar(k)),C(bar(i)-3bar(j)+2bar(k)) and D(bar(i)-bar(j)+2bar(k)) then the vector equation plane parallel to bar(ABC) and passing the centroid of the tetrahedron ABCD is

If A(2bar(i)-bar(j)-3bar(k)), B(4bar(i)+bar(j)-bar(k)), C(bar(i)-3bar(j)+2bar(k)), D(bar(i)-bar(j)-2bar(k)) then the vector equation of the plane parallel to bar(ABC) and passing through the centroid of the tetra-hedron ABCD is

If A(3bar(i)+2bar(j)-bar(k)), B(2bar(i)-2bar(j)+5bar(k)), C(bar(i)+3bar(j)-bar(k)) then vector equation of the line passing through the centroid of DeltaABC and parallel to bar(BC) is

If 2bar(i)-bar(j)+bar(k), bar(i)-3bar(j)-5bar(k), 3bar(i)-4bar(j)-4bar(k) are the vertices of a triangle then the vector equation of the median passing through 2bar(i)-bar(j)+bar(k) is

The vectors 2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+bar(j)-2bar(k)

If A(bar(i)+2bar(j)+3bar(k)), B(-bar(i)-bar(j)+8bar(k)), C(-4bar(i)+4bar(j)+6bar(k)) are the vertices of a triangle then the equation of the line passing through the circumcentre and parallel to bar(AB) is

If bar(a) = bar(i) - bar(j)-bar(k), bar(b) = 2bar(i) - 3bar(j) + bar(k) then find the projection vector of bar(b) on bar(a) and its magnitude.

If bar(a)=bar(i)+2bar(j)+2bar(k) and bar(b)=3bar(i)+6bar(j)+2bar(k) then the vector in the direction of bar(a) and having magnitude as abs(bar(b)) is