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Examples: Equation of a Plane Perpendicular to a given Vector and passing through a given point Video Lecture | Mathematics (Maths) for JEE Main & Advanced
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FAQs on Examples: Equation of a Plane Perpendicular to a given Vector and passing through a given point Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 1. What is the equation of a plane perpendicular to a given vector and passing through a given point? |  |
Ans. The equation of a plane perpendicular to a given vector and passing through a given point can be determined using the dot product. Let's say the given vector is represented by the components (a, b, c) and the given point is (x0, y0, z0). The equation of the plane can be written as ax + by + cz = d, where d = ax0 + by0 + cz0.
| 2. How can I find the normal vector of a plane given its equation? | |
Ans. The normal vector of a plane can be determined directly from its equation. If the equation of the plane is ax + by + cz = d, then the coefficients (a, b, c) give the components of the normal vector. Thus, the normal vector can be written as (a, b, c).
| 3. Can a plane have more than one normal vector? | |
Ans. No, a plane cannot have more than one normal vector. The normal vector of a plane is unique and is perpendicular to the plane. Any vector that is perpendicular to the plane can be considered as the normal vector, but they are all equivalent in terms of their direction and magnitude.
| 4. If a plane is parallel to a coordinate axis, what can we say about its normal vector? | |
Ans. If a plane is parallel to a coordinate axis, then its normal vector will be perpendicular to that particular axis. For example, if a plane is parallel to the x-axis, then its normal vector will have the form (0, b, c), where b and c can be any real numbers.
| 5. How can I determine if two planes are parallel or perpendicular to each other? | |
Ans. Two planes are parallel if their normal vectors are parallel or proportional to each other. In other words, the cross product of their normal vectors will be zero or the components of the normal vectors will be in the same ratio. Two planes are perpendicular if their normal vectors are perpendicular to each other, which means their dot product will be zero.
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Nov 21, 2024 Last updated |
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