Let - - b- - - are three unit vectors such that - - b- - - is also a unit vector- If pairwise angles - - b- - - are -1 - -2 and - 3 respectively then cos-1 - cos-2 - cos-3 equals -

The correct option is A 1 |â+b̂+ĉ| = 1 Squaring both sides we get, (â.â+b̂.b̂+ĉ.ĉ + 2(â.b̂+b̂.ĉ+ĉ.â)) = 1 Since |â| = |b̂| = |ĉ| =1 ⇒ (3+2(c ...

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Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

Let â , b̂ ...

Question

Let $^a,^b,^c$ are three unit vectors such that $^a +^b +^c$ is also a unit vector. If pairwise angles $^a,^b,^c$ are $θ_{1}, θ_{2}$ and $θ_{3}$ respectively then $cos θ_{1} + cos θ_{2} + cos θ_{3}$ equals :

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Solution

The correct option is A -1
$|^a +^b +^c | = 1$

Squaring both sides we get,

$(^a .^a +^b .^b +^c .^c + 2 (^a .^b +^b .^c +^c .^a)) = 1$

Since $|^a | = |^b | = |^c | = 1$

$\Rightarrow (3 + 2 (c o s θ_{1} + c o s θ_{1} + c o s θ_{3})) = 1$

$\Rightarrow (c o s θ_{1} + c o s θ_{2} + c o s θ_{3}) = - 1$

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Let ^a,^b,^c are three unit vectors such that ^a+^b+^c is also a unit vector. If pairwise angles ^a,^b,^c are θ1,θ2 and θ3 respectively then cosθ1+cosθ2+cosθ3 equals :

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