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If 2 vec A C = 3 vec C B , then prove th...

If 2` vec A C` = 3` vec C B` , then prove that 2` vec O A` =3` vec C B` then prove that 2` vec O A` + 3` vec O B` =5` vec O C` where `O` is the origin.

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To solve the problem, we need to prove that if \( 2 \vec{A} \vec{C} = 3 \vec{C} \vec{B} \), then \( 2 \vec{O} \vec{A} + 3 \vec{O} \vec{B} = 5 \vec{O} \vec{C} \), where \( O \) is the origin. ### Step-by-Step Solution: 1. **Understand the Given Relation**: We are given that: \[ 2 \vec{A} \vec{C} = 3 \vec{C} \vec{B} ...
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