If a - - -2-k- b -2- - -k- and c -3- -k- then find the scalars m and n such that m a -n b-

a⃗=î+ĵ 2k̂ b⃗=2î ĵ+k̂ c⃗=3î k̂ ma⃗+nb⃗=c⃗ mî+mĵ 2mk̂+2nî nĵ+nk̂=3î k̂ (m+2n)î+(m n)ĵ+( 2m+n)k̂3î k̂ By equating corresponding coef ...

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Convexity

If a =î +ĵ ...

Question

If $\to a =^i +^j -^2 k$ , $\to b =^2 i -^j +^k$ and $\to c =^3 i -^k$ , then find the scalars m and n such that $m \to a + n \to b$ .

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Solution

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¯ ¯ ¯ a =^i +^j - 2^k, ¯ ¯ b = 2^i -^j +^k

¯ ¯ c = 3^i +^k

¯ ¯ c = m ¯ ¯ ¯ a + n ¯ ¯ b

\to a =^i +^j - 2^k

\to b = 2^i -^j +^k

\to c = 3^i -^k

m

n

\to c = m \to a + n \to b

¯ ¯ ¯ a =^i +^j - 2^k, ¯ ¯ b = 2^i - 0^j +^k, ¯ ¯ c = 3^i -^k

¯ ¯ c = m ¯ ¯ ¯ a + n ¯ ¯ b

m + n =

m_{1}, m_{2}, m_{3}, m_{4}

_{1} =^2 i -^j +^k

_{2} =^3 i -^4 j -^4 k

_{3} = -^i +^j -^k

_{4} = -^i +^3 j +^k

\to a =^i +^j +^k, \to b =^i -^j +^k, \to c =^2 i +^3 j -^k

(\to a \times \to b) \times \to c =

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