If A- - B- - C- and the magnitudes of A- - B- C- are 5-4- and 3 units- then the angle between A- and C- is

The correct option is A cos^ 1(35) | A⃗ #160; | =5 | B⃗ #160; | =4 | C⃗ #160; | =? given : #160; A⃗ =B⃗ +C⃗ A⃗ C⃗ =B⃗ | A⃗ ...

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

Byju's Answer

Standard XII

Physics

Vector Addition

If A⃗ = B⃗ ...

Question

If $\to A = \to B + \to C$ , and the magnitudes of $\to A$ , $\to B$ , $\to C$ are $5, 4$ , and $3$ units, then the angle between $\to A$ and $\to C$ is

{cos}^{- 1} (\frac{3}{5})

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

{cos}^{- 1} (\frac{4}{5})

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

{sin}^{- 1} (\frac{3}{4})

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!

Open in App

Solution

The correct option is A ${cos}^{- 1} (\frac{3}{5})$
$∣ ∣ \to A ∣ ∣ = 5 ∣ ∣ \to B ∣ ∣ = 4 ∣ ∣ \to C ∣ ∣ = ?$
given : $\to A = \to B + \to C$
$\to A - \to C = \to B$
$∣ ∣ \to A - \to C ∣ ∣ = ∣ ∣ \to B ∣ ∣$
${∣ ∣ \to A ∣ ∣}^{2} + {∣ ∣ \to C ∣ ∣}^{2} - 2 ∣ ∣ \to A ∣ ∣ ∣ ∣ \to C ∣ ∣ cos θ = {∣ ∣ \to B ∣ ∣}^{2}$
$25 + 9 - 2 \times 5 \times 3 cos θ = 16$
$cos θ = \frac{18}{30}$
$θ = {cos}^{- 1} (\frac{3}{5})$

Suggest Corrections

Similar questions

The magnitudes of vectors $\to A, \to B a n d \to C$ are 3, 4 and 5 units respectively. If $\to A + \to B = \to C$ , the angle between $\to A$ and $\to B$ is

Q. If

\to A = \to B + \to C

and the magnitude of

\to A, \to B

and

\to C

are

5, 4

and

3

units, respectively, then the angle between

\to A

and

\to C

is:

The magnitude of vector $\to A, \to B$ and $\to C$ are respectively 12, 5 and 13 units and $\to A + \to B = \to C$ then the angle between $\to A$ and $\to B$ is