SOLUTION: OP = <6,5>, OQ = <13, &#8722;2>, u = i &#8722; 3j and v = 3i &#8722; 2j. If PQ = ku + hv where k and h are constant, find a)k and h Hint: PQ = PO + OQ). k & h already get answer

Algebra ->  Functions -> SOLUTION: OP = <6,5>, OQ = <13, &#8722;2>, u = i &#8722; 3j and v = 3i &#8722; 2j. If PQ = ku + hv where k and h are constant, find a)k and h Hint: PQ = PO + OQ). k & h already get answer      Log On


   



Question 150803: OP = <6,5>, OQ = <13, −2>, u = i − 3j and v = 3i − 2j. If PQ = ku + hv
where k and h are constant, find
a)k and h Hint: PQ = PO + OQ).
k & h already get answer k=1 & h=2....
b)Unit vector for PQ in terms of i and j??

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a)k=1, h=2 is correct
b)PQ=(13-6,-2-5)=(7,-7)
To find the unit vector, find the magnitude of the vector and divide the vector by it.
abs%28PQ%29=sqrt%28%287%29%5E2%2B%28-7%29%5E2%29
abs%28PQ%29=sqrt%282%287%29%5E2%29
abs%28PQ%29=7%2Asqrt%282%29
u%5BPQ%5D=PQ%2Fabs%28PQ%29
u%5BPQ%5D=(7%2F%287%2Asqrt%282%29%29,-7%2F%287%2Asqrt%282%29%29)
u%5BPQ%5D=(1%2F%28sqrt%282%29%29,-1%2F%28sqrt%282%29%29)
u%5BPQ%5D=(sqrt%282%29%2F2,-sqrt%282%29%2F2)
u%5BPQ%5D=%28sqrt%282%29%2F2%29i-%28sqrt%282%29%2F2%29j