Câu `47:`

Ta có : `vec{BD'} = vec{BA} + vec{A A'} + vec{A'D'}`

` = -vec{AB} + vec{A A'} + vec{AD}`

`vec{MN} = vec{MC} + vec{C C'} + vec{C'N}`

` = 1/3 vec{AC} + vec{C C'} + x vec{C'D}`

` = 1/3 (vec{AB} + vec{AD}) + vec{C C'} + x(vec{C'C} + vec{CD})`

` = 1/3 vec{AB} + 1/3 vec{AD} + vec{C C'} - x vec{C C'} + x vec{CD}`

` = 1/3 vec{AB} + 1/3 vec{AD} + (1 - x) vec{C C'} - x vec{AB}`

` = (1/3 - x) vec{AB} + 1/3 vec{AD} + (1 - x) vec{C C'}`

` = (1/3 - x) vec{AB} + 1/3 vec{AD} + (1 - x) vec{A A'}`

Để `MN //// BD'`

`to -(1/3 - x)/1 = 1/3 = (1 - x)/1 to x = 2/3`