CameraIcon

SearchIcon

MyQuestionIcon

255

You visited us 255 times! Enjoying our articles? Unlock Full Access!

Applications of Dot Product

Let a⃗ and ...

Question

Let $\to a$ and $\to b$ be two given vectors such that $| \to a | = \sqrt{3}, | \to b | = 2$ and $\to a \cdot \to b = \sqrt{6} .$ Find the angle between $\to a$ and $\to b .$

Open in App

Solution

$\begin{matrix} L e t θ b e t h e a n g l e b e t w e e n \to a a n d \to b . T h e n, \to a . \to b = \sqrt{6} \Rightarrow ∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ cos θ = \sqrt{6} \Rightarrow (\sqrt{3}) (2) cos θ = \sqrt{6} \Rightarrow cos θ = \frac{\sqrt{6}}{2 \sqrt{3}} \Rightarrow cos θ = \frac{1}{\sqrt{2}} \Rightarrow θ = {cos}^{- 1} (\frac{1}{\sqrt{2}}) = \frac{π}{4} H e n c e, t h e r e q u i r e d a n g l e i s \frac{π}{4} . \end{matrix}$

Hence, this is the answer.

Suggest Corrections

thumbs-up

0

Similar questions

\to a

\to b

are two vectors, such that

\to a \cdot \to b < 0

| \to a \cdot \to b | = | \to a \times \to b |

, then the angle between vectors

\to a

\to b

| \to a - \to b |

, if two vectors

\to a

\to b

| \to a | = 2

| \to b | = 3

\to a . \to b = 4

\to a

\to b

be two vectors such that

| \to a | = 1,

| \to b | = 4

\to a \cdot \to b = 2.

\to c = (2 \to a \times \to b) - 3 \to b,

then the angle between

\to b

\to c

\to a

\to b

are two vectors, such that

| \to a | = 3

| \to b | = 2

\to a - \to b

is unit vector, then the acute angle between

\to a

\to b

\to a

\to b

| \to a + \to b | = | \to a - \to b |

. What is the angle between

\to a

\to b

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Dot Product

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Applications of Dot Product

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon