Let a- and b- be two unit vectors such that a-b- is also a unit vector- Then the angle between a- and b- is

The correct option is D 2π3 nbsp; nbsp;a and b are unit vectors. ⇒ |a|=|b|=1 Also, nbsp; a + b is a unit vector. ⇒ |a + b|^2=1 ⇒ |a|^2+ |b|^2+2 a·b=1 ⇒ ...

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

Byju's Answer

Standard XII

Physics

Unit Vectors

Let a⃗ and b⃗...

Question

Let $\to a$ and $\to b$ be two unit vectors such that $\to a + \to b$ is also a unit vector. Then the angle between $\to a$ and $\to b$ is

\frac{π}{6}

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

\frac{π}{3}

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

\frac{π}{2}

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

\frac{2 π}{3}

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

Open in App

Solution

The correct option is D $\frac{2 π}{3}$
$\to a$ and $\to b$ are unit vectors.
$\Rightarrow | \to a | = | \to b | = 1$
$Also, \to a + \to b$ is a unit vector.
$\Rightarrow | \to a + \to b |^{2} = 1$
$\Rightarrow | \to a |^{2} + | \to b |^{2} + 2 \to a \cdot \to b = 1$
$\Rightarrow 1^{2} + 1^{2} + 2 \times 1 \times 1 \times cos θ = 1$
$\Rightarrow cos θ = \frac{- 1}{2}$
$\Rightarrow θ = \frac{2 π}{3}$

Suggest Corrections

Similar questions

Q. If

\to a

and

\to b

are two unit vectors such that

\to a + \to b

is also a unit vector, then find the angle between

\to a

and

\to b .

Q. Let

\to a

and

\to b

are two vectors, such that

| \to a | = 3

and

| \to b | = 2

. If

\to a - \to b

is unit vector, then the acute angle between

\to a

and

\to b

is ______

Q. Let the vectors

\to a

and

\to b

be such that

| \to a | = 3

and

| \to b | = \frac{\sqrt{2}}{3}

, then

\to a \times \to b

is a unit vector, if the angle between

\to a

and

\to b

Q. Let

\to a

and

\to b

be two unit vectors such that angle between them is

60^{o}

. Then

| \to a - \to b |

is equal to.

Q. If

\to a & \to b

are unit vectors, then angle between

\to a

and

\to b

for

\sqrt{3} \to a - \to b

to be unit vector is

Join BYJU'S Learning Program

Let →a and →b be two unit vectors such that →a+→b is also a unit vector. Then the angle between →a and →b is

The correct option is D 2π3 →a and →b are unit vectors. ⇒|→a|=|→b|=1 Also, →a+→b is a unit vector. ⇒|→a+→b|2=1 ⇒|→a|2+|→b|2+2→a⋅→b=1 ⇒12+12+2×1×1×cosθ=1 ⇒cosθ=−12 ⇒θ=2π3

Let $\to a$ and $\to b$ be two unit vectors such that $\to a + \to b$ is also a unit vector. Then the angle between $\to a$ and $\to b$ is