# point of intersection

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.

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#### Solution Preview

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

Angle CAF=

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 . ...

#### Solution Summary

This solution finds the coordinates of the point of intersection.