1) Points P and Q have position vectors OP = 5i - 3j + 2k andOQ = 2i+ 3j, respectively. Find the vectorQP, and determine its direction cosines. Hence find the unit
vector in the direction of QP.
2) Find the direction cosines of the vector joining the point
(-2,2,8) (i.e., x = ¡2, y = 2, z = 8) to the point (1,0,2).
3) Find the parametric vector and Cartesian equations of
the line with direction cosines (2/7,-3/7, 6/7) which
passes through the point A with position vector i + 2j -k.
Calculate the coordinates of the point where the line
meets the plane x = -1. A second line passes through
the points B and C with respective coordinates (3,-2, 1)
and (2, 1, 4). Find the Cartesian parametric equations of
this line and show that the two lines intersect. Calculate
the coordinates of the point of intersection.
4) In a Cartestian coordinate system, point A is given by
(-3, 0,-5) and 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 coordinates of D.
Find a vector that is perpendicular to both AB and CD.