Please find vector GY in terms of vector GI and GZ by elementary vector properties.Point I divides line segment YZ (arrow on top) in a 2:3 Ratio. Point G is any point outside the given line. Please...

Please find vector GY in terms of vector GI and GZ by elementary vector properties.

Point I divides line segment YZ (arrow on top) in a 2:3 Ratio. Point G is any point outside the given line. Please find vector GY (arrow on top) in terms of vector GI and GZ (both arrow on top) by elementary vector properties.

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Asked on by juno60

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to write the vector `bar (IY)`   in terms of vectors `bar (GI) ` and `bar (GY) ` such that:

`bar (IY) +bar (GY) = bar (GI) =gt bar (IY) = bar (GI) - bar (GY)`

You need to write the vector `bar (IZ)`  in terms of vectors `bar (GI)`  and `bar (GZ)`  such that:

`bar (IZ) = bar (ZG) + bar (GI)`

You need to remember that the problem provides the information `(bar(YI))/(bar (IZ)) = 2/3 =gt bar (IY) = (2/3)bar(ZI)`

You need to substitute `bar (GZ) + bar(IG)`  for `bar(ZI)`  and `bar (GI) - bar (GY) ` for `bar (IY)`  such that:

`bar (GI) - bar (GY) = (2/3) (bar (GZ)+bar (IG))`

`bar (GY) = bar (GI) + (2/3)bar (ZG) + (2/3)bar (GI)`

`bar (GY) = (5bar (GI )+ 2bar (ZG))/3`

`bar (GY) = (5 bar (GI)- 2bar (GZ))/3`

Hence, evaluating `bar (GY) ` in terms of `bar (GI) ` and `bar (GZ) ` yields `bar (GY) = (5 bar (GI) - 2bar (GZ))/3.`

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