Please help on below questions

Kindly show all steps

EQUATION OF PLANE QUESTIONS With respect to the origin O, the points A, B and C have position vectors given by OA = i-k, OB = 31 + 2j -3k and OC = 41 - 3j + 2k. The mid-point of AB is M. The point N lies on AC between A and C and is such that AN = 2NC. (i) Find a vector equation of the line MN. [4] (ii) It is given that MN intersects BC at the point P. Find the position vector of P. [4] 2 The lines / and m have vector equations r = i+j + k+ s(i -j + 2k) and r = 4i + 6j + k +/(2i + 2j + k) respectively. (i) Show that / and m intersect. [4] (ii) Calculate the acute angle between the lines. [3] 3 With respect to the origin O, the points A and B have position vectors given by OA = i + 2j + 2k and OB = 3i + 4j. The point P lies on the line AB and OP is perpendicular to AB. (i) Find a vector equation for the line AB. [1] (ii) Find the position vector of P. [4] 4 With respect to the origin O, the lines / and m have vector equations r = 2i + k + >(i - j + 2k) and r = 2j + 6k + H(i+ 2j - 2k) respectively. (i) Prove that / and m do not intersect. [4] (ii) Calculate the acute angle between the directions of / and m. [3] points A and B are given by OA = i + 2j + 2k