Question

The position vectors of p and q are p=i-3j and q=4i+5j respectively. Find the unit vector parallel to pq .?

Answer 1

`color(blue)(3/sqrt(73)bbi+8/sqrt(73)bbj)`

Explanation:

`bbp=bbi-3bbj`

`bbq=4bbi+5bbj`

`vec(pq)=bbq-bbp`

`\ \ \ \ \ =4bbi+5bbj-(bbi-3bbj)=3bbi+8bbj`

A unit vector in the direction of some vector `bba` is given by:

`bbhata=(bb(a))/||bb(a)||`

`:.`

`bb(hat(pq))=(bb(pq))/(||bb(pq)||`

`||bb(pq)||=sqrt((3)^2+(8)^2)=sqrt(73)`

`bb(hat(pq))=(3bbi+8bbj)/sqrt(73)=3/sqrt(73)bbi+8/sqrt(73)bbj`

So a unit vector in the direction of `vec(pq)` is:

`color(blue)(3/sqrt(73)bbi+8/sqrt(73)bbj)`