NCERT solution Class 11 introduction to three dimensional geometry

NCERT Solutions

Class 11 Maths

Introduction to Three Dimensional Geometry

NCERT Questions

Ex.12.1 Q.1
Ex.12.1 Q.2
Ex.12.1 Q.3
Ex.12.1 Q.4
Ex.12.2 Q.1
Ex.12.2 Q.2
Ex.12.2 Q.3
Ex.12.2 Q.4
Ex.12.2 Q.5
Ex.12.3 Q.1
Ex.12.3 Q.2
Ex.12.3 Q.3
Ex.12.3 Q.4
Ex.12.3 Q.5
Misc. Q.1
Ex.Misc. Q.2
Ex.Misc. Q.3
Ex.Misc. Q.4
Ex.Misc. Q.5
Ex.Misc. Q.6

Ex.12.3 Q.1

Find the coordinates of the point which divides the line segment joining the points (–2, 3, 5) and (1, –4, 6) in the ratio

(1) 2: 3 internally,

(2) 2: 3 externally.

(1) The coordinates of point R that divides the line segment joining points P (x₁, y₁, z₁) and

Q (x₂, y₂, z₂) internally in the ratio m: n is

{(mx₂ + nx₁) ÷ (m + n), (my₂ + ny₁) ÷ (m + n), (mz₂ + nz₁) ÷ (m + n)}

Let R (x, y, z) be the point that divides the line segment joining points (–2, 3, 5) and (1, –4, 6)

internally in the ratio 2 : 3 x = {2 × 1 + 3 × (-2)} ÷ (2 + 3)

= (2 - 6) ÷ 5 = - y = {2 × (-4) + 3 × 3} ÷ (2 + 3)

= (-8 + 9) ÷ 5 = z = (2 × 6 + 3 × 5) ÷ (2 + 3) = (12 + 15) ÷ 5 =

Thus, the coordinates of the required point are (- , , ).

(2) The coordinates of point R that divides the line segment joining points P (x₁, y₁, z₁) and Q (x₂, y₂, z₂) internally in the ratio m: n is

{(mx₂ - nx₁) ÷ (m - n), (my₂ - ny₁) ÷ (m - n), (mz₂ - nz₁) ÷ (m - n)}

Let R (x, y, z) be the point that divides the line segment joining points (–2, 3, 5) and (1, –4, 6)

externally in the ratio 2 : 3 x = {2 × 1 - 3 × (-2)} ÷ (2 - 3)

= (2 + 6) ÷ (-1) = -8 y = {2 × (-4) - 3 × 3} ÷ (2 - 3)

= (-8 - 9) ÷ (-1) = 17 z = (2 × 6 - 3 × 5) × (2 - 3) = (12 - 15) ÷ (-1) = 3

Thus, the coordinates of the required point are (–8, 17, 3).

Introduction to Three Dimensional Geometry Class 11 Maths NCERT Chapter 11 NCERT Solutions

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