How would you solve the following vector question:
In a cartestian coordinate system, point A is given by (-3, 0, -5) and a point B by (3, 4, 3). Find the direction cosines of the line AB and write down the vector equation for this line.
A second line passes through point C with coordinates (2, 5, 5), and is in the direction (2i + 3j + 6k). show that these two lines intersect at a point D and write down the coordinate of D.
Find a vector that is perpendicular to both AB and CD.