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

Since a⃗ + λb⃗ is ⊥ to c⃗ , (a⃗ + λb⃗).c⃗ #160;= 0 ∴ (2î + 2ĵ + 3k̂ λî + 2λĵ + λk̂ ).(3î + ĵ) = 0 ∴ 3(2 λ) + (2 + 2λ) + 0 ...

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Applications of Dot Product

If a⃗ = 2î ...

Question

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

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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 + 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}

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

\to C = 3^i +^j

\to A + t \to B

\to C

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