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Question

The coordinates of the point which divides the line segment joining the points (1, –2, 3) and (3, 4, –5) internally in the ratio 2:3 is (x, y, z). Find the value of x+y+z
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Solution

The coordinates of the point P which divides the line segment joining two points A(x1,y1,z1) and B(x2,y2,z2) internally in the ratio m:n are (mx2+nx1m+n,my2+ny1m+n,mz2+nz1m+n)
Let P(x, y, z) be the point which divides line segment joining A(1, –2, 3) and B(3, 4, –5) internally in the ratio 2:3 therefore,
x=2(3)+3(1)2+3=95
y=2(4)+3(2)2+3=25
z=2(5)+3(3)2+3=15
x+y+z = 95+25+15
= 2

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