Let -b- be unit vectors and - - - are angles between the vectors -b-b- and - respectively- If -b- is also a unit vector then cos- -cos- -cos- is equal to

The correct option is B 1 |â + nbsp;b̂ + nbsp;ĉ| = 1 ⇒ a^2 + b^2 + c^2 + 2(â.b̂ + nbsp;b̂.ĉ + nbsp;â.ĉ) = 1 ⇒ nbsp;(â.b̂ + nbs ...

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Standard X

Mathematics

Section Formula

Let â,b̂,ĉ ...

Question

Let $^a,^b,^c$ be unit vectors and $α, β, γ$ are angles between the vectors $^a,^b;^b,^c$ and $^c,^a$ respectively. If $^a +^b +^c$ is also a unit vector then $cos α + cos β + cos γ$ is equal to

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Solution

The correct option is B $- 1$
$|^a +^b +^c | = 1$
$\Rightarrow a^{2} + b^{2} + c^{2} + 2 (^a .^b +^b .^c +^a .^c) = 1$
$\Rightarrow (^a .^b +^b .^c +^a .^c) = - 1$
$\Rightarrow cos α + cos β + cos γ = - 1$

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Let ^a,^b,^c be unit vectors and α,β,γ are angles between the vectors ^a,^b;^b,^c and ^c,^a respectively. If ^a+^b+^c is also a unit vector then cosα+cosβ+cosγ is equal to

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Let $^a,^b,^c$ be unit vectors and $α, β, γ$ are angles between the vectors $^a,^b;^b,^c$ and $^c,^a$ respectively. If $^a +^b +^c$ is also a unit vector then $cos α + cos β + cos γ$ is equal to

The correct option is B $- 1$
$|^a +^b +^c | = 1$
$\Rightarrow a^{2} + b^{2} + c^{2} + 2 (^a .^b +^b .^c +^a .^c) = 1$
$\Rightarrow (^a .^b +^b .^c +^a .^c) = - 1$
$\Rightarrow cos α + cos β + cos γ = - 1$