If `4bar(i) + (2p)/3 bar(j)+ pbar(k)` is parallel to the vector `bar(i) + 2bar(j) + 3bar(k)`, find p.

Find the vector equation of the plane which passes through the points 2bar(i)+4bar(j)+2bar(k), 2bar(i)+3bar(j)+5bar(k) and parallel to the vector 3bar(i)-2bar(j)+bar(k) . Also find the point where this plane meets the line joining the points 2bar(i)+bar(j)+3bar(k) and 4bar(i)-2bar(j)+3bar(k) .

Find the vector equation of the line passing through the point 2bar(i)+3bar(j)+bar(k) and parallel to the vector 4bar(i)-2bar(j)+3bar(k)

The vector equation of the plane passing through the points bar(i)-2bar(j)+bar(k),3bar(k)-2bar(j) and parallel to the vector 2bar(i)+bar(j)+bar(k) is

Find the equation of the line passing through the point 2bar(i)+3bar(j)-4bar(k) and parallel to the vector 6bar(i)+3bar(j)-2bar(k) in cartesian form.

Find the vector equation of the plane passing through the point bar(i)+bar(j)+bar(k) and parallel to the vectors 2bar(i)+3bar(j)+4bar(k), bar(i)-2bar(j)+3bar(k) .