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Asked by araima2001 | 19th Mar, 2017, 09:02: AM

Expert Answer:

begin mathsize 16px style the space condition space for space the space lines space straight x equals az plus straight b comma space straight y equals space cz plus straight d space and space straight x equals straight a 1 straight z plus straight b comma space straight y equals space straight c 1 straight z plus straight d space to space be space perpendicular space is space meritnation
The space equations space of space the space first space line space are
straight x equals az plus straight b space and space space straight y equals space cz plus straight d
rightwards double arrow fraction numerator straight x minus straight b over denominator straight a end fraction equals straight z over 1 equals fraction numerator straight y minus straight d over denominator straight c end fraction space space... left parenthesis straight i right parenthesis
The space equations space of space the space second space line space are
straight x equals straight a subscript 1 straight z plus straight b subscript 1 space and space space straight y equals space straight c subscript 1 straight z plus straight d subscript 1
rightwards double arrow fraction numerator straight x minus straight b subscript 1 over denominator straight a subscript 1 end fraction equals straight z over 1 equals fraction numerator straight y subscript 1 minus straight d subscript 1 over denominator straight c subscript 1 end fraction space space... left parenthesis ii right parenthesis
So comma space from space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space can space see space that space the space direction space consines space of space the space two space lines space are
proportional space to space straight a comma space 1 comma space straight c comma space straight a subscript 1 comma space 1 comma space straight c subscript 1.
bold italic R bold italic e bold italic c bold italic a bold italic l bold italic l bold comma bold space bold italic t bold italic h bold italic e bold space bold italic s bold italic t bold italic r bold italic a bold italic i bold italic g bold italic h bold italic t bold space bold italic l bold italic i bold italic n bold italic e bold italic s bold space bold italic a bold italic x bold space bold plus bold space bold italic b bold italic y bold space bold plus bold space bold italic c bold space bold equals bold space bold 0 bold space bold italic a bold italic n bold italic d bold space bold italic a bold ’ bold italic x bold space bold plus bold space bold italic b bold ’ bold italic y bold space bold plus bold space bold italic c bold ’ bold space bold equals bold space bold 0 bold space bold italic a bold italic r bold italic e bold space bold italic a bold italic t bold space bold italic r bold italic i bold italic g bold italic h bold italic t bold space bold italic a bold italic n bold italic g bold italic l bold italic e bold italic s bold space bold italic i bold italic f bold italic f bold space bold italic a bold italic a bold ’ bold space bold plus bold space bold italic b bold italic b bold ’ bold space bold equals bold space bold 0 bold.
So comma space the space two space lines space are space perpendicular space if
straight a times straight a subscript 1 plus 1 times 1 plus straight c times straight c subscript 1 equals 0
rightwards double arrow aa subscript 1 plus cc subscript 1 plus 1 equals 0 end style

Answered by Rebecca Fernandes | 19th Mar, 2017, 02:19: PM