If a-2-2-3k-b-2-3k-c-3- are such that a-b- is perpendicular to c- then find value of -

We have #160; a #160; = 2i + 2j + 3k b #160; = #160; i + 2j + 3k c #160; = 3i + j Now, a #160; + αb #160; = ( 2 α)i + ( 2 + ...

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Applications of Dot Product

If a⃗=2î+2ĵ...

Question

If $\to a = 2^i + 2^j + 3^k, \to b = -^i + 2^j + 3^k \to c = 3^i +^j$ are such that $\to a + α \to b$ is perpendicular to $\to c$ then find value of $α$

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

\to c = 3^i +^j

\to a + λ \to b

\to c

λ

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

\to c = 3^i +^j

\to a + λ \to b

\to c

λ

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

\to b = 3^i + 2^j +^k

\to c =^i -^j - 4^k

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

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

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

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

\to c = 3^i +^j

\to a + t \to b

\to c

t

\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}

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