Cho hình hộp $ABCD.A_1{B}_1{C}_1{D}_1$. Mệnh đề nào sau đây đúng?

(AI giải đề cho tôi)
A đúng: $\overrightarrow{BA}+\overrightarrow{BC}=\overrightarrow{BD}$, rồi $\overrightarrow{BD}+\overrightarrow{B{B}_1}=\overrightarrow{B{D}_1}$, nên $\left|\overrightarrow{BA}+\overrightarrow{B{B}_1}+\overrightarrow{BC}\right|=\left|\overrightarrow{B{D}_1}\right|$. B sai: $\overrightarrow{A{A}_1}+\overrightarrow{C_{1}D}+\overrightarrow{C_1{D}_1}=\overrightarrow{A{A}_1}+\overrightarrow{D_{1}D}+\overrightarrow{C_1{D}_1}=\overrightarrow{AD}+\overrightarrow{C_1{D}_1}=\overrightarrow{BC}+\overrightarrow{D_1{A}_1}\ne \vec{0}$. C sai: $\overrightarrow{A{B}_1}-\overrightarrow{A{D}_1}=\overrightarrow{D_1{B}_1}=\overrightarrow{DA}$, độ dài bằng $|DA|\ne |B{D}_1|$. D sai: $\overrightarrow{A{B}_1}+\overrightarrow{A{D}_1}=\overrightarrow{AB}+\overrightarrow{A{A}_1}+\overrightarrow{AD}+\overrightarrow{A{A}_1}=\overrightarrow{A{C}_1}+\overrightarrow{A{A}_1}\ne \overrightarrow{A{C}_1}$.