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Question
In the triangle PQR, `bar"PQ" = bar"2a", bar"QR" = bar"2b"`. The midpoint of PR is M. Find the following vectors in terms of `bar"a"` and `bar"b"`:
(i) `bar"PR"` (ii) `bar"PM"` (iii) `bar"QM"`.
Solution
`bar"PQ" = bar"2a" , bar"QR" = bar"2b"`
(i) `bar"PR" = bar"PQ" + bar"QR"`
`= 2bar"a" + 2barb`
(ii) ∵ M is the midpoint of PR
∴ `bar"PM" = 1/2bar"PR"`
`= 1/2[2bar"a" + 2bar"b"]`
`= bar"a" + bar"b"`
(iii) `bar"RM" = 1/2(bar"RP") = - 1/2 bar"PR"`
`= - 1/2(2bar"a" + 2bar"b")`
`= - bar"a" - bar"b"`
∴ `bar"QM" = bar"QR" + bar"RM"`
`= 2bar"b" - bar"a" - bar"b"`
`= bar"b" - bar"a"`
Notes
Point (i) answer in the textbook is incorrect.
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