Figure in attachment shows a cuboid OABCDEFG, where O is the origin. A has position vector 5i, C has position vector 10j and D has position vector 20k.
(a) Find the cosine of angle CAF.
Given that the point X lies on AC and that FX is perpendicular to AC,
(b) find the position vector of point X and the distance FX.
The line l1 passes through O and through the midpoint of the face ABFE. The line l2 passes through A and through the midpoint of the edge FG.
(c) Show that l2 and l2 intersect and find the coordinates of the point of intersection.© BrainMass Inc. brainmass.com December 16, 2022, 1:10 am ad1c9bdddf
From the given information, the position vectof of F is given by
a) for the angle CAF, we consider the vecors AC and AF which are given by and
b) the direction ratios of the vector AC are -5, 10 ie -1, 2, 0
Any point X on the line AC is given by . ...
This solution finds the coordinates of the point of intersection.