Find the coordinates of the point which divides the line segment joining the points (1,−2,3)(1, -2, 3)(1,−2,3) and (3,4,−5)(3, 4, -5)(3,4,−5) in the ratio 2:32:32:3 internally.
Here (x1,y1,z1)=(1,−2,3)(x_1, y_1, z_1) = (1, -2, 3)(x1,y1,z1)=(1,−2,3), (x2,y2,z2)=(3,4,−5)(x_2, y_2, z_2) = (3, 4, -5)(x2,y2,z2)=(3,4,−5), m=2,n=3m=2, n=3m=2,n=3. x=2(3)+3(1)2+3=6+35=95x = \frac{2(3) + 3(1)}{2+3} = \frac{6+3}{5} = \frac{9}{5}x=2+32(3)+3(1)=56+3=59 y=2(4)+3(−2)2+3=8−65=25y = \frac{2(4) + 3(-2)}{2+3} = \frac{8-6}{5} = \frac{2}{5}y=2+32(4)+3(−2)=58−6=52 z=2(−5)+3(3)2+3=−10+95=−15z = \frac{2(-5) + 3(3)}{2+3} = \frac{-10+9}{5} = -\frac{1}{5}z=2+32(−5)+3(3)=5−10+9=−51 Point: (95,25,−15)(\frac{9}{5}, \frac{2}{5}, -\frac{1}{5})(59,52,−51).
Find the ratio in which the YZ-plane divides the line segment formed by joining the points (−2,4,7)(-2, 4, 7)(−2,4,7) and (3,−5,8)(3, -5, 8)(3,−5,8).
Point Coordinates
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