If the vectors a-2k-b-2-4-k- and c-k- are mutually orthogonal- then - -

The correct option is B ( 3,2) Since a⃗ , b⃗ and c⃗ are mutually orthogonal then a⃗.b⃗=0 , #160; b⃗.c⃗=0 , #160; c⃗.a⃗=0 ...

Linear Combination of Vectors

If the vector...

Question

If the vectors $\to a =^i -^j + 2^k, \to b = 2^i + 4^j +^k$ and $\to c = λ^i +^j + μ^k$ are mutually orthogonal, then $(λ, μ) =$

(2, - 3)

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(- 2, 3)

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(3, - 2)

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(- 3, 2)

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Solution

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

\to b = 2^i + 4^j +^k

\to c = λ^i +^j + μ^k

(λ, μ) =

\to a = 2^i + 4^j - 5^k, \to b =^i +^j +^k, \to c =^j + 2^k

\to a + \to b + \to c

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

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

\to c =^i +^j -^k

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

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

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

\to b = 2^i - 4^j - 3^k, \to c = -^i + 2^j + 2^k

\to a + \to b + \to c = 4^i - 4^j

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

\to a + 2 \to b - 3 \to c

\sqrt{78}

\to a^{'} =^i +^j, \to b^{'} =^i +^j + 2^k

\to c^{'} = 2^i +^j -^k

\to a, \to b, \to c

\to b

\to c

(\to a, \to b, \to c

{\to a}^{'}, {\to b}^{'}, {\to c}^{'}

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