Find Value of |(vec(a) xx vec(c)) * vec(b)|

abkapseln87 2022-10-11 Answered
If a and b are two unit vectors and c be a vector such that 2 ( a × b ) + c = b × c . Then maximum value of | ( a × c ) b |
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Answers (1)

Cody Petty
Answered 2022-10-12 Author has 6 answers
Let c = α a + β b + γ a × b
b × c = α b × a + β b × b + γ b × ( a × b ) = α a × b + γ [ ( b b ) a ( b a ) b ] = γ a γ ( a b ) b α a × b
2 ( a × b ) + c = α a + β b + ( γ + 2 ) a × b
Therefore, γ = α, γ ( a b ) = β and α = γ + 2
Solving, α = γ = 1 and β = a b
So, c = a + ( a b ) b a × b
c c = a a + ( a b ) 2 ( b b ) + ( a × b ) ( a × b ) 2 ( a b ) ( a b ) | c | 2 = 1 ( a b ) 2 + | a × b | 2 = 2 | a × b | 2
and its greatest value is 2.
The greatest value of | ( a × c ) b | is 1.
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