Find the coordinates of the point that divides the join of A(-2, 4, 7) and B(3, - 5, 8) extremally in the ratio 2 : 1.
The coordinates of point $R$ that divides the line segment joining points $P\left(x_{1}\right.$, $\left.\mathrm{y}_{1}, \mathrm{z} 1\right)$
and $Q\left(x_{2}, y_{2}, z_{2}\right)$ externally in the ratio $m: n$ are
$\left(\frac{m x_{2}-n x_{1}}{m-n}, \frac{m y_{2}-n y_{1}}{m-n}, \frac{m z_{2}-n z_{1}}{m-n}\right)$
Point $A(-2,4,7)$ and $B(3,-5,8), m$ and $n$ are 2 and 1 respectively.
Using the above formula, we get,
$\left(\frac{2 \times 3-1 \times-2}{2-1}, \frac{2 \times-5-1 \times 4}{2-1}, \frac{2 \times 8-1 \times 7}{2-1}\right)$
$=(8,-14,9)$, is the point that divides the two point $A$ and $B$ externally in the ratio $2: 1$.
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,