The equation of the line passing through $(-4,3,1)$, parallel to the plane $x+2 y-z-5=0$
and intersecting the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z-2}{-1}$ is:
$\frac{x+4}{-1}=\frac{y-3}{1}=\frac{z-1}{1}$
$\frac{x+4}{3}=\frac{y-3}{-1}=\frac{z-1}{1}$
$\frac{x+4}{1}=\frac{y-3}{1}=\frac{z-1}{3}$
$\frac{x-4}{2}=\frac{y+3}{1}=\frac{z+1}{4}$
Correct Option: , 2
Normal vector of plane containing two intersecting lines is parallel to vector.
$\left(\overrightarrow{\mathrm{V}}_{1}\right)=\left|\begin{array}{ccc}\hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ 3 & 0 & 1 \\ -3 & 2 & -1\end{array}\right|$
$=-2 \hat{\mathrm{i}}+6 \hat{\mathrm{k}}$
$\therefore$ Required line is parallel to vector
$\left(\overrightarrow{\mathrm{V}}_{2}\right)=\left|\begin{array}{ccc}\hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ 1 & 2 & -1 \\ -2 & 0 & 6\end{array}\right|=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$
$\Rightarrow$ Required equation of line is
$\frac{x+4}{3}=\frac{y-3}{-1}=\frac{z-1}{1}$
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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,