If a- b- and c- are three unit vectors such that a-b-c- is also a unit vector and -1- -2 and -3 are angles between the vectors- respectively- then among -1- -2 and -3-

The correct option is B at least one is obtuse angle|a⃗ + b⃗ + c⃗| = 1 ⇒ (a⃗ + b⃗ + c⃗). (a⃗ + b⃗ + c⃗) = 1 ⇒a⃗.b⃗ + b⃗. c⃗ + c⃗ . a⃗ = 1 ⇒ cosθ_1 + cosθ_2 + ...

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Byju's Answer

Standard XII

Physics

Work Done as Dot Product

If a⃗, b⃗ and...

Question

If $\to a, \to b$ and $\to c$ are three unit vectors such that $\to a + \to b + \to c$ is also a unit vector and $θ_{1}, θ_{2}$ and $θ_{3}$ are angles between the vectors , respectively, then among $θ_{1}, θ_{2}$ and $θ_{3}$ .

all are acute angles

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all are right angles

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at least one is obtuse angle

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atleast two of them are equal

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Solution

The correct option is C at least one is obtuse angle
$| \to a + \to b + \to c | = 1 \Rightarrow (\to a + \to b + \to c) . (\to a + \to b + \to c) = 1 \Rightarrow \to a . \to b + \to b . \to c + \to c . \to a = - 1 \Rightarrow c o s θ_{1} + c o s θ_{2} + c o s θ_{3} = - 1$
So, at least one of $θ_{1}, θ_{2}$ and $θ_{3}$ must be negative

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If →a,→b and →c are three unit vectors such that →a+→b+→c is also a unit vector and θ1,θ2 and θ3 are angles between the vectors , respectively, then among θ1,θ2 and θ3 .

The correct option is C at least one is obtuse angle|→a+→b+→c|=1⇒(→a+→b+→c).(→a+→b+→c)=1⇒→a.→b+→b.→c+→c.→a=−1⇒cosθ1+cosθ2+cosθ3=−1 So, at least one of θ1,θ2 and θ3 must be negative

If $\to a, \to b$ and $\to c$ are three unit vectors such that $\to a + \to b + \to c$ is also a unit vector and $θ_{1}, θ_{2}$ and $θ_{3}$ are angles between the vectors , respectively, then among $θ_{1}, θ_{2}$ and $θ_{3}$ .