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Find the equation of the plane through the points (2, 1, 0), (3, –2, –2), and (3, 1, 7).

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

    Since,  the  equation  of  the  plane  passing  through  the  points  (x1, y1, z1),(x2, y2, z2)  and  (x3, y3, z3)  is ⇒             | x − x 1 y − y 1 z − z 1 x 2 − x 1 y 2 − y 1 z 2 − z 1 x 3 − x 1 y 3 − y 1 z 3 − z 1 | = 0 ⇒                         | x − 2 y − 1 z − 0 3 − 2 − 2 − 1 − 2 − 0 3 − 2 1 − 1 7 − 0 | = 0 ⇒                                               | x − 2 y − 1 z 1 − 3 − 2 1 0 7 | = 0 ⇒ ( x − 2 ) | − 3 − 2 0 7 | − ( y − 1 ) | 1 − 2 1 7 | + z | 1 − 3 1 0 | = 0 ⇒                                     ( x − 2 ) ( − 2 1 ) − ( y − 1 ) ( 7 + 2 ) + z ( 3 ) = 0 ⇒                                                                           − 2 1 ( x − 2 ) − 9 ( y − 1 ) + 3 z = 0 ⇒                                                                                       − 2 1 x + 4 2 − 9 y + 9 + 3 z = 0 ⇒   − 2 1 x − 9 y + 3 z + 5 1 = 0         ⇒ 7 x + 3 y − z − 1 7 = 0 H e n c e ,     t h e     r e q u i r e d     e q u a t i o n     i s     7 x + 3 y − z − 1 7 = 0

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