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 + ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

all are right angles

No worries! We‘ve got your back. Try BYJU‘S free classes today!

at least one is obtuse angle

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

atleast two of them are equal

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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

Suggest Corrections

Similar questions

Q. 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 the angles between the vectors

\to a, \to b;

\to b, \to c

and

\to c, \to a

, then

Q. Let

\to a, \to b, \to c

are three unit vectors such that

\to a + \to b + \to c

is also a unit vector. If pairwise angles between

\to a, \to b, \to c

are

θ_{1}, θ_{2} a n d θ_{3}

respectively then

c o s θ_{1} + c o s θ_{2} + c o s θ_{3}

equals

Q. Let

\to a, \to b, \to c

be three unit vectors such that

\to b \times (\to c \times \to a) = \frac{\to c}{2} .

\to a

and

\to c

are non-parallel, then the angles which

\to b

makes with

\to c

and

\to a

are respectively

Q. Let

\to a, \to b, \to c

be three units vectors such that

\to a \times (\to b \times \to c) = \frac{\to b + \to c}{\sqrt{2}}

and the angles between

\to a, \to c

and

\to a, \to b

α

and

β

respectively, then

Q. If

\to a, \to b

and

\to c

are unit vectors such that

\to a + \to b + \to c = 0

, then the angle between

\to a

and

\to b

Join BYJU'S Learning Program

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 $θ_{3}$ .