Let α → = 4 i ^ + 3 j ^ + 5 k ^ and β → = i ^ + 2 j ^ - 4 k ^ . Let β → 1 be parallel to α → and β → 2 be perpendicular to α → . If β → = β → 1 + β → 2 , then the value of 5 β → 2 · i ^ + j ^ + k ^ is

Step-by-step solution

Given that α → = 4 i ^ + 3 j ^ + 5 k ^ and β → = i ^ + 2 j ^ - 4 k ^ and β → = β 1 → + β 2 → ⇒ β 2 → = β → - β 1 →   . . . . . . . . . . 1 since β → 1 is parallel to α → , β 1 → = t α → ⇒ β 1 → = t 4 i ^ + 3 j ^ + 5 k ^ = 4 t i ^ + 3 t j ^ + 5 t k ^   . . . . . . . . . 2 Substituting the values of β 1 → and α → in ( 1 ) , we get &#