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

Question

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, Only P and Q, Only P and R, Only Q and R, All P , Q & R

MARKS App · Accepted Answer

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 satisfy the line joining u → & v → .

Search any question & find its solution

Looking for more such questions to practice?