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If P,Q,R are three points with respective position vectors i+j,i-j and ai+bj+ck.The points P,Q,R are collinear,if
Asked by g_archanasharma | 15 Apr, 2019, 05:59: PM
answered-by-expert Expert Answer
G i v e n colon space P equals i plus j comma space Q equals i minus j space a n d space R equals a i plus b j plus c k N o w comma space p o i n t s space P comma space Q space a n d space R space a r e space c o l l i n e a r space i s space stack P Q with rightwards arrow on top cross times stack Q R with rightwards arrow on top equals 0 space stack P Q with rightwards arrow on top equals left parenthesis i minus j right parenthesis minus left parenthesis i plus j right parenthesis equals negative 2 j space a n d space stack Q R with rightwards arrow on top equals a i plus b j plus c k minus left parenthesis i minus j right parenthesis equals left parenthesis a minus 1 right parenthesis i plus left parenthesis b plus 1 right parenthesis j plus c k stack P Q with rightwards arrow on top cross times stack Q R with rightwards arrow on top equals 0 rightwards double arrow open vertical bar table row i j k row 0 cell negative 2 end cell 0 row cell a minus 1 end cell cell b plus 1 end cell c end table close vertical bar equals 0 rightwards double arrow i left parenthesis negative 2 c right parenthesis minus j left parenthesis 0 right parenthesis plus k left parenthesis 2 a minus 2 right parenthesis equals 0 rightwards double arrow negative 2 c i plus 2 left parenthesis a minus 1 right parenthesis k equals 0 H e n c e comma space P comma space Q space a n d space R space a r e space c o l l i n e a r space i f space minus 2 c i plus 2 left parenthesis a minus 1 right parenthesis k equals 0
Answered by Renu Varma | 16 Apr, 2019, 10:08: AM

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