Question

If |A+B| = A.B . What is the angle between the two vectors. If A and B are two vectors ​

Answer 1

Explanation:

The angle between two vectors $A$ and $B$ is $\theta $ . Vector $R$ is the resultant of the two vectors.

Answer 2

Explanation:

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Questions & Answers

CBSE

Physics

Grade 11

Scalar And Vector Quantities

Question

Answers

Related Questions

The angle between two vectors A and B is θ .Vector R is the resultant of the two vectors. If R makes an angle θ2 with A, then

A.)A=2B

B.)A=B2

C.)A=B

D.AB=1

Answer

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Hint – You can start the solution by drawing a well-labelled diagram with all the vectors (A,BandR) originating from a common point. The equations for the magnitude of the resultant vector and the direction of the resultant vector are R=A2+B2+2ABCosθ−−−−−−−−−−−−−−−−−√ and tanα=BsinθA+Bcosθ respectively. Use the second equation given above to reach the solution.

Complete answer:

To solve this equation, consider the diagram given below

The arrangement of A, B and R (Resultant) vectors is done in such a way that it is easy to co-relate with the other two vectors.

We know,

∠AOB=θ,

And ∠ROA=θ2

We also know,

∠BOR=∠AOB−∠ROA

⇒∠BOR=θ−θ2

⇒∠BOR=θ2

The equation for the ∠ROA is as follows –

tanα=BsinθA+Bcosθ

⇒sin(θ2)cos(θ2)=2B(θ2)cos(θ2)A+Bcosθ

⇒A+Bcosθ=Bcos2θ(θ2)

⇒A+B[2cos2(θ2)−1]=2Bcos2(θ2)

⇒A=B

Hence, Option C is the correct option

Additional Information:

A vector is a mathematical quantity that has both a magnitude (size) and a direction