Ive yr 2 mathematics

I want the following question step please ^ __ ^ .

Q.1

Given OA = 4i=3j and C is a point on OA such that │OC│= 16/5
a) Find the unit vector in the direction of OA.
b) Hence find OC.
c) If OB = i=4j , show that BC is perpendicular to OA .


Q.2

A boat has a speed of 7km per hour and is set to head north-east but a tide of 2km per hour flows from a north west direction . What is the actual speed and direction of the boat ?

Q.3

a) Find a unit vector parallel to the resultant of the vectors a= (2,4,-5) and b=(1,2,3).
b) If O is the origin and OP=(2,3,-1), OQ= (4,-3,2) . Find PQ and determine its magnitude.

Q.4

A force , F=4i=5j-2k , causes a body to move from point A , with coordinates (1,-2,5) , to point B , with coordinates (-2,1,-3) . The origin O has coordinates (0,0,0)

Find:
a) The displacement of the body , AB
b) the work done by the force.