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Sum
In the given figure express `bar"c"` and `bar"d"` in terms of `bar"a"` and `bar"b"`.
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Solution
`bar"PQ" = bar"PS" + bar"SQ"`
∴ `bar"a" = bar"c" - bar"d"` ...(1)
`bar"PR" = bar"PS" + bar"SR"`
∴ `bar"b" = bar"c" + bar"d"` ....(2)
Adding equations (1) and (2), we get
`bar"a" + bar"b" = (bar"c" - bar"d") + (bar"c" + bar"d") = 2bar"c"`
∴ `bar"c" = 1/2 (bar"a" + bar"b") = 1/2 (bar"a" + bar"b")`
`= (2bar"b" - (bar"a" + bar"b"))/2`
`= 1/2(bar"b" - bar"a") = 1/2bar"b" - 1/2bar"a"`
Hence, `bar"c" = 1/2 bar"a" + 1/2bar"b"` and `bar"d" = 1/2bar"b" - 1/2bar"a"`
Concept: Vectors and Their Types
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