1) reffered to a fixed point origin O, the positional vector of points P and Q are (-2i+3j) and ( ki + lj ) respectively, where k and l are constants. The point M is the midpoint of PQ. given the position vector of M relative to O is (2i+4j)
a) find the values of k and l
the point R is such that PQ : QR = 1:2
b)find, in terms of i and j, the expression for OR
Wayne DeguMan
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a) [(-2 + k)i/2, (3 + l)j/2] = (2i + 4j)
=> -2 + k = 4...i.e. k = 6
and 3 + l = 8...i.e. l = 5
so, OQ is 6i + 5j
b) PQ = OQ - OP = (6i + 5j) - (-2i + 3j) = 8i + 2j
and QR = OR - OQ = (ai + bj) - (6i + 5j)
Now, (ai + bj) - (6i + 5j) = 2(8i + 2j)
=> (ai + bj) - (6i + 5j) = 16i + 4j
so, (a - 6)i + (b - 5)j = 16i + 4j
=> a - 6 = 16.....i.e. a = 22
and b - 5 = 4.....i.e. b = 9
so, OR is (22i + 9j)
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