Let u → = 2 i ^ + j ^ and v → = 3 i ^ - 5 j ^ . Consider three points P , Q and R having the position vectors 5 2 i ^ - 2 j ^ , 7 3 i ^ - j ^ and 9 4 i ^ respectively. Among these, the points in the line passing through u → and v → are

Step-by-step solution

Given that: u → = 2 i ^ + j ^ and v → = 3   i ^ - 5   j ^ ⇒ u ( 2 , 1 )   &   v ( 3 , - 5 ) Three points P ( 5 2 , - 2 ) ,   Q ( 7 3 , - 1 ) and R ( 9 4 , 0 ) Line passing through u   and   v : y - y 1 = y 2 - y 1 x 2 - x 1 ( x - x 1 ) y - 1 = - 5 - 1 3 - 2 ( x - 2 ) y - 1 = - 6 x + 12 6 x + y = 13 Put P ( 5 2 , - 2 ) ,   Q ( 7 3 , - 1 )   &   R ( 9 4 , 0 ) P :   15 - 2 - = 13 Q :   14 - 1 = 13 R :   27 4 + 0 ≠ 13 P , Q