[问答题]
The position vectors of the points A, B and C are a,
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t 9pr4vabh c18gy*, gqt97bv oy, relative to an origin O.The following diagram shows the triangle ABC and points N, R, S and
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N is a point on $ [\mathrm{AB}] $ such that $ \overrightarrow{\mathrm{AN}}=\frac{3}{7} \overrightarrow{\mathrm{AB}}$ .
R is a point on $[\mathrm{BC}]$ such that $\overrightarrow{\mathrm{BR}}=\frac{2}{5} \overrightarrow{\mathrm{BC}} $.
S is a point on $[\mathrm{CA}] $ such that $\overrightarrow{\mathrm{CS}}=\frac{2}{5} \overrightarrow{\mathrm{CA}}$ .
T is a point on $[\mathrm{RS}] $ such that $ \overrightarrow{\mathrm{RT}}=\frac{2}{3} \overrightarrow{\mathrm{RS}}$ .
1. 1. Express $\overrightarrow{\mathrm{AN}}$ in terms of $\mathbf{a} $ and $\mathbf{b}$ .
2. Hence show that $ \overrightarrow{\mathrm{CN}}=\frac{4}{7} \mathbf{a}+\frac{3}{7} \mathbf{b}-\mathbf{c}$ .
2. 1. Express $ \overrightarrow{\mathrm{RC}}$ in terms of $\mathbf{b}$ and $\mathbf{c} $ and $ \overrightarrow{\mathrm{CS}} $ in terms of $ \mathbf{a}$ and $\mathbf{c}$ .
2. Hence show that $\overrightarrow{\mathrm{RT}}=\frac{4}{15} \mathbf{a}-\frac{6}{15} \mathbf{b}+\frac{2}{15} \mathbf{c} $.
3. Prove that T lies on $[\mathrm{CN}]$ .
