a = 4 i ^ + 13 j ^ − 18 k ^ , b = i ^ − 2 j ^ + 3 k ^ and c = 2 i ^ + 3 j ^ − 4 k ^ are three vectors such that a = x b + y c , then x + y =

Question

a = 4 i ^ + 13 j ^ ​ − 18 k ^ , b = i ^ − 2 j ^ ​ + 3 k ^ and c = 2 i ^ + 3 j ^ ​ − 4 k ^ are three vectors such that a = x b + y c , then x + y =, -1, -2, 5, 1

MARKS App · Accepted Answer

$ ​ a = x b + y c ∴ 4 i ^ + 13 j ^ ​ − 18 k ^ = ( i ^ − 2 j ^ ​ + 3 k ^ ) ( x ) + ( 2 i ^ + 3 j ^ ​ − 4 k ^ ) ( y ) = ( x + 2 y ) i ^ + ( − 2 x + 3 y ) j ^ ​ + ( 3 x − 4 y ) k ^ ∴ x + 2 y = 4 , − 2 x + 3 y = 13 and 3 x − 4 y = − 18 ​ S o l v in g , w e g e t x=-2, y=3 \Rightarrow x+y=1$

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