1) PointsPandQhave position vectorsOP= 5i - 3j + 2kandOQ= 2i+ 3j, respectively. Find the vectorQP, and determine its direction cosines. Hence find the unit

vector in the direction ofQP.

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 pointAwith position vector i + 2j -k.

Calculate the coordinates of the point where the line

meets the planex= -1. A second line passes through

the pointsBandCwith 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 lineABand 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 bothABandCD.