Three vectors A- - - - 2- - 3 k- - B- - - - 2- - k- and C- - 3 - - - are given- If A- - t B- is perpendicular to C- then- t is

A⃗ + tB⃗ = î+ 2ĵ + 3 k̂ + t( î + 2ĵ + k̂) = nbsp; (1 t)î + (2 + 2t)ĵ + (3+t) k̂ (A⃗ + B⃗). C⃗ = 0 3(1 t) +(2+2t)=0 t = 5 sec ...

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Multiplication with Vectors

Three vectors...

Question

Three vectors $\to A =^i + 2^j + 3^k, \to B = -^i + 2^j +^k$ and $\to C = 3^i +^j$ are given. If $\to A + t \to B$ is perpendicular to $\to C$ then, t is

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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 + t \to b

\to c

t

\to a = (1, x, - 2)

\to b = (x, 3, - 4)

x = 2

\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

t = 5

\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 + λ \to b

\to c

λ

\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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