Section Formula in 3D Geometry

Chapter 11 Class 11 - Intro to Three Dimensional Geometry
Serial order wise

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### Transcript

Question 1 Find the coordinates of the point which divides the line segment joining the points (β2, 3, 5) and (1, β4, 6) in the ratio (i) 2:3 internally. Let A be (β2, 3, 5) & B be (1, β4, 6) Let coordinate of point P be (x, y, z) that divides the line joining A & B in the ratio of 2 : 3 internally We know that Coordinate of P that divide the line segment joining A(x1, y1, z1) & B(x2, y2, z2) internally in the ratio m: n is P(x, y, z) = ((γπ π₯γ_2+γ π π₯γ_1)/(π + π),(γπ π¦γ_2 +γ π π¦γ_1)/(π + π),(γπ π§γ_(2 )+γ π π§γ_1)/(π + π)) Here, x1 = β 2, y1 = 3, z1 = 5 x2 = 1, y2 = β 4, z2 = 6 & m = 2 , n = 3 Putting values (x, y, z) = ((2(1) + 3(β2))/(2+3),(2 (β4) + 3(3))/(2+ 3),(2(6) + 3(5))/(2+ 3)) = ((2 β 6)/5,(β 8 + 9)/5,(12 + 15)/( 5)) = ((β4)/( 5),1/5,27/( 5)) Thus, the required coordinate of point P is ((βπ)/( π),π/π,ππ/( π))