Question

AB is straight line where vec (AB)=8a-10b. M is the midpoint of AB. Express vec (AM) in terms of a and b. Give your answer in its simplest form.

Answer 1

Vector AM, when AB is a straight line and M is the midpoint of AB, is expressed as the simplified form 4a - 5b, which is half of vector AB (8a - 10b).

Step-by-step explanation:

To express vector AM in terms of a and b when given that vector AB is 8a - 10b and M is the midpoint of AB, we need to find half of vector AB. Since M is the midpoint, vector AM will be half of vector AB. Therefore, to calculate vector AM, we divide vector AB by 2:

vector AM = ½ * vector AB
= ½ * (8a - 10b)
= 4a - 5b.

So, vector AM in its simplest form is 4a - 5b.