6.8.12 Distance of a point from a plane
Chapter 6: Chapter 6 · MATHEMATICS-VOLUME 1 · EN medium
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(a) Equation of a plane in vector form Theorem . The perpendicular distance from a point with position vector u to the plane r n is given by u n δ Proof Let A be the point whose position vector is u . Applications of Vector Algebra Let F be the foot of the perpendicular from the point A to the plane r n . The line joining F and A is parallel to the normal vector n hence its equation is r u tn . But F is the point of intersection of the line r u tn and the given plane r n . If r is the position vector of F , then u t n for some t ∈ , and r n .Eliminating r we get u t n which implies u n Now,
📖 Class 12 Mathematics English Volume 1 2025 Edition www.tntextbooks.in · Page 276
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(a) Equation of a plane in vector form Theorem . The perpendicular distance from a point with position vector u to the plane r n is given by u n δ Proof Let A be the point whose position vector is u . Applications of Vector Algebra Let F be the foot of the perpendicular from the point A to the plane r n . The line joining F and A is parallel to the normal vector n hence its equation is r u tn .
But F is the point of intersection of the line r u tn and the given plane r n . If r is the position vector of F , then u t n for some t ∈ , and r n .Eliminating r we get u t n which implies u n Now,
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