A=-2,-3,3B=13,-3,133PA=2PB3AP=2PBAPPB=23By section formulaP=mx2+nx1m+n, my2+ny1m+n, mz2+nz1m+nThereforeP=2×13+3×-22+3, 2×-3+3×-32+3, 2×13+3×32+3P=205, -155, 355P=4,-3,7

Solve 14

A = (- 2, - 3, 3) B = (13, - 3, 13) 3 P A = 2 P B 3 A P = 2 P B \frac{A P}{P B} = \frac{2}{3} B y s e c t i o n f o r m u l a P = (\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n}, \frac{m z_{2} + n z_{1}}{m + n}) T h e r e f o r e P = (\frac{2 \times 13 + 3 \times (- 2)}{2 + 3}, \frac{2 \times (- 3) + 3 \times (- 3)}{2 + 3}, \frac{2 \times 13 + 3 \times 3}{2 + 3}) P = (\frac{20}{5}, \frac{- 15}{5}, \frac{35}{5}) P = (4, - 3, 7)

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