The scalar product of the vector a → = i ^ + j ^ + k ^ with a unit vector along the sum of the vectors b → = 2 i ^ + 4 j ^ - 5 k ^ and c → = λ i ^ + 2 j ^ + 3 k ^ is equal to one. Then. λ =

Step-by-step solution

Given, a → = i ^ + j ^ + k ^   . . . i b → = 2 i ^ + 4 j ^ - 5 k ^ c → = λ i ^ + 2 j ^ + 3 k ^ Now, b → + c → = λ + 2 i ^ + 6 j ^ - 2 k ^ Let unit vector b → be the vector along b → + c → b → = ( λ + 2 ) i ^ + 6 j ^ - 2 k ^ ( λ + 2 ) 2 + 36 + 4 ⇒ b → = ( λ + 2 ) i ^ + 6 j ^ - 2 k ^ ( λ + 2 ) 2 + 40 . . . i i Now, a → · b → = 1 ⇒ i ^ + j ^ + k ^ .   ( λ + 2 ) i ^ + 6 j ^ - 2 k ^ ( &#9