Vector functions

[anonuser0511]

p527 essential specialist mathematics
Q22c)

[A hiker starts from a point defined by the position vector -7i +2j and travels at the rate of 6km/h along as line parallel to the vector 4i +3j. The units in the frame of reference are in kilometres.]

The path of a cyclist along a straight road is defined simultaneously by the vector equation
b(t) = (7t - 4)i + (9t - 1)j
i) Find the position of the hiker when she reaches the road.
ii) Find the time taken by the hiker to reach the road.
iii) Find, in terms of t, the distance between the hiker and the rider t seconds after the start.
iv) Find the shortest distance between the hiker and the rider, correct to 2 d.p.

would be cool if someone could direct me to a place in the book where this type of Q is solved/ show me working which i can apply to similar Qs

[kamil9876]

To solve this you need to know:

*how to antidifferentiate/differentiate vector functions
*Be comfortable with the concept of direction and how it relates to the velocity vector.
*Finding Cartesian Form
*Distance between two points.
*Optional: How to find shortest distance between two curves using geometry/tangents.

If you know all the above(except the last dot point, that is optional) then your only issue may be knowing how to apply this, in that case it is preferable that you tell us what you tried/are unsure of and we can point you in the right direction.