6.9 Image of a Point in a Plane
Chapter 6: Chapter 6 · MATHEMATICS-VOLUME 1 · EN medium
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Let A be the given point whose position vector is u . Let r n be the equation of the plane. Let v be the position vector of the mirror image A ′ of A in the plane. Then ' AA is perpendicular to the plane. So it is parallel to n . Then AA ′ = or v u ⇒ v u ... ( ) Let M be the middle point of AA ′ . Then the position vector of M is u v . But M lies on the plane. So, u v ⋅ ... ( ) Sustituting ( ) in ( ), we get u u ⋅ ⇒ u Therefore, the position vector of A ′ is [ )] u n v u Note The mid point of M of AA ′ is the foot of the perpendicular from the point A to the plane r n . So the position vector of the foot M of the perpendicular is given by .
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 281
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Let A be the given point whose position vector is u . Let r n be the equation of the plane. Let v be the position vector of the mirror image A ′ of A in the plane. Then ' AA is perpendicular to the plane.
So it is parallel to n . Then AA ′ = or v u ⇒ v u ... ( ) Let M be the middle point of AA ′ . Then the position vector of M is u v .
But M lies on the plane. So, u v ⋅ ... ( ) Sustituting ( ) in ( ), we get u u ⋅ ⇒ u Therefore, the position vector of A ′ is [ )] u n v u Note The mid point of M of AA ′ is the foot of the perpendicular from the point A to the plane r n . So the position vector of the foot M of the perpendicular is given by .
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