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If position vectors of A and B are a and b respectively, then mid-point of AB has position vector
Aa − b
B(a + b)
C(a + b)/3
D(a + b)/2
Answer & Solution
Correct answer: D. (a + b)/2
1. Section formula: the point dividing AB in ratio m : n has position vector (na + mb)/(m + n).
2. For mid-point, m = n = 1: ((1)a + (1)b)/2.
3. Hence the mid-point's position vector is (a + b)/2.
_Source: Maharashtra Balbharati Std XII Mathematics Part 1, Ch 5 "Vectors" §5.3_
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