Hey shan2391
The question is dealing with vectors and states this:
The points P, Q and R are such that QR = 4PQ. Given that the position vectors of P and Q relative to an
origin O are (6i + 7j) and (9i + 20j) respectively, find the unit vector parallel to OR.
Really simple question.
Let me break it down for you,
first they are asking you to find, the unit vector parallel to OR....
ok, so lets find the position vector of OR first,
To make the question easier,
lets just call it ( xi + yj )
The question also states that QR = 4PQ
What is QR ?
( xi + yj ) - ( 9i + 20j )
This statement can join to give single component vectors:
QR => (x - 9)i + (y - 20)j
Next, what is 4PQ?
4[ ( 9i + 20j ) - (6i + 7j) ]
=> 4[3i + 13j]
12i + 52j
ok,
now equate the equation:
(x - 9)i + (y - 20)j = 12i + 52j
and solve for the i's and j's separetely
therefore,
x - 9 = 21
x = 21
and
y - 20 = 52
y = 72
Giving us a position vector for R ( 21 i + 72 j)
Finding the unit vector is the easy bit
1/Magnitude of the vector * (21 i + 72 j )
=> (21 i + 72 j) / 75