If vectors a- and b- are such that -a-3- -b-23 and a-b- is a unit vector- then write the angle between a- and b-

| a⃗×b⃗ #160; | =1 ⇒| a | | b | sinθ #160; =1 =3× 2 3 sinθ #160; =1⇒sinθ #160; = 1 2 ∴θ =30 #176; ...

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

Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

If vectors ...

Question

If vectors $\to a$ and $\to b$ are such that $| \to a | = 3, | \to b | = \frac{2}{3}$ and $\to a \times \to b$ is a unit vector, then write the angle between $\to a$ and $\to b$

Open in App

Solution

$∣ ∣ \to a \times \to b ∣ ∣ = 1$
$\Rightarrow | a | | b | sin θ = 1$
$= 3 \times \frac{2}{3} sin θ = 1 \Rightarrow sin θ = \frac{1}{2}$
$∴ θ = 30 °$

Suggest Corrections

Similar questions

Q. If vectors

\to a

and

\to b

are such that,

| \to a | = 3, | \to b | = \frac{2}{3}

and

\to a \times \to b

is a unit vector, then write the angle between

\to a

and

\to b .

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. If two vectors

\to a

and

\to b

are such that

| \to a . \to b | = | \to a \times \to b |

, tyhen find the angle between the vectors

\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

\to a

and

\to b

be unit vectors such that

| \to a + \to b | = \sqrt{3}

. Then the value of

(2 \to a + 5 \to b) \cdot (3 \to a + \to b + \to a \times \to b)

Join BYJU'S Learning Program

If vectors →a and →b are such that |→a|=3, |→b|=23 and →a×→b is a unit vector, then write the angle between →a and →b

∣∣→a×→b∣∣=1⇒|a||b|sinθ=1=3×23sinθ=1⇒sinθ=12∴θ=30°

If vectors $\to a$ and $\to b$ are such that $| \to a | = 3, | \to b | = \frac{2}{3}$ and $\to a \times \to b$ is a unit vector, then write the angle between $\to a$ and $\to b$

$∣ ∣ \to a \times \to b ∣ ∣ = 1$
$\Rightarrow | a | | b | sin θ = 1$
$= 3 \times \frac{2}{3} sin θ = 1 \Rightarrow sin θ = \frac{1}{2}$
$∴ θ = 30 °$