The position vector of point A is 2i - k and the equation of the line is:

r = (-7i, 15j, -5k) + s(3i, -7j, 4k), sER

Determine the position vectors of B and C, both lying on the line such that the length AB = AC = 10.

Given that the point P is the midpoint of BC, show that the equation of the plane 1, which contains the line and is perpendicular to AP is r . (-3i, j, 4k) = t where t is an integer to be determined.

The planes 2 and 3 have the equations:

r . (i, 2j, -3k) = 5 and r . (i, -2j, k) respectively

a) Verify that A lies in both 2 and 3

b) Determine the point D, the point of intersection between 1, 2 and 3

c) Find the volume of the tetrahedron ABCD

The answer for the position vectors of B and C are given as: Vector OB = (-4i, 8j, -k) and Vector OC = (2i, -6j, 7k) There is no answer given for the value of t in the question asks to determine t The answer for b) is Vector OD = (15i, 13j, 12k) The answer for c) is 962/3 where the volume of the tetrahedron has a formula of 1/3 * base area * perpendicular height

I have all the answers, but I'm not sure how to solve for them