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Dot Product of Two Vectors

vec a vec b v...

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vec a vec b vec c are unit vectors not all co-linear such that vec a timesvec c=vec c timesvec b and vec b timesvec a=vec a timesvec c. alpha beta gamma are the angles between vec a and vec b vec b and c vec c and vec a respectively.If 4(cos alpha+cos beta+cos gamma)+t=0 then value of t is

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\to a, \to b, \to c

be vectors of equal magnitude such that the angle between

\to a

\to b

α, \to b

\to C

β

\to c

\to a

γ

. Then, the minimum value of

cos α + cos β + cos γ

a (\to α \times \to β) + b (\to β \times \to γ) + c (\to γ \times \to α) = \to 0

and atleast one of

a, b, c

are non-zero then the vectors

\to α, \to β, \to γ

\to a, \to b, \to c

be three unit vectors such that

∣ ∣ \to a + \to b + \to c ∣ ∣ = 1

\to a ⊥ \to b

\to c

α, β

\to a, \to b

respectively then

cos α + cos β

a (\to α \times \to β) + b (\to β \times \to γ) + c (\to γ \times \to α) = \to 0

a, b, c

is non zero, then vectors,

\to α, \to β, \to γ

α (\to a \times \to b) + β (\to b \times \to c) + γ (\to c \times \to a) = \to 0

and at least one of the scalars

α, β, γ

is non-zero, then the vectors

\to a, \to b, \to c

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