Consider three vectors A = i + j − 2 k , B = i ^ − j ^ + k ^ and C = 2 i ^ − 3 j ^ + 4 k ^ . A vector X of the form α A + βB ( α and β are numbers) is perpendicular to C. The ratio of α and β is

Question

Consider three vectors A = i + j − 2 k , B = i ^ − j ^ ​ + k ^ and C = 2 i ^ − 3 j ^ ​ + 4 k ^ . A vector X of the form α A + βB ( α and β are numbers) is perpendicular to C. The ratio of α and β is

TestHub · Accepted Answer

Vector X of the form α A + β B X X ​ = α A + β B = α ( i ^ + j ^ ​ − 2 k ^ ) + β ( i ^ − j ^ ​ + k ^ ) = i ^ ( α + β ) + j ^ ​ ( α − β ) + k ^ ( − 2 α + β ) ​ A vector X is perpendicular to C , i.e., X ⋅ C = 0 or − 9 α + 9 β = 0 or α = β or β α ​ = 1 1 ​ or α : β = 1 : 1

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