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Find the equation of a plane which bisects perpendicularly the line joining the points A(2, 3, 4) and B(4, 5, 8) at right angles.

0 2 Views | Posted 3 months ago
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    Answered by

    Payal Gupta | Contributor-Level 10

    3 months ago

    This is a short answer type question as classified in NCERT Exemplar

    T h e     g i v e n     t h a t     A ( 2 ,   3 ,   4 )     a n d     B ( 4 ,   5 ,   8 ) Coordinates  of  mid−point  C  are  (2+42, 3+52, 4+82)=(3, 4, 6) N o w     d i r e c t i o n     r a t i o s     o f     t h e     n o r m a l     t o     t h e     p l a n e = d i r e c t i o n     r a t i o s     o f     A B                                                                                                                           = 4 − 2 ,     5 − 3 ,     8 − 4 = ( 2 ,   2 ,   4 ) E q u a t i o n     o f     t h e     p l a n e     i s                                   a ( x − x 1 ) + b ( y − y 1 ) + c ( z − z 1 ) = 0 ⇒                                     2 ( x − 3 ) + 2 ( y − 4 ) + 4 ( z − 6 ) = 0 ⇒                                                           2 x − 6 + 2 y − 8 + 4 z − 2 4 = 0 ⇒                                                                                                             2 x + 2 y + 4 z = 3 8 ⇒                                                                                                                         x + y + 2 z = 1 9 H e n c e ,     t h e     r e q u i r e d     e q u a t i o n     o f     p l a n e     i s                   x + y + 2 z = 1 9     o r     r → ( i ^ + j ^ + 2 k ^ ) = 1 9 .

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