Physics, asked by kypify, 9 months ago

Magnitude of vector and vector b are 5 and 5root3 respectively. angles between vectors is 90 degrees. What is the value of the angle between resultant vector and vector A?

Answers

Answered by hayarunnisamuhammedp
3

Answer:

Let P and Q be two vectors acting simultaneously at a point and represented both in magnitude and direction by two adjacent sides OA and OD of a parallelogram OABD as shown in figure.

Let θ be the angle between P and Q and R be the resultant vector. Then, according to parallelogram law of vector addition, diagonal OB represents the resultant of P and Q.

So, we have

R = P + Q

Now, expand A to C and draw BC perpendicular to OC.

From triangle OCB,

OB

2

=C

2

+BC

2

or OB

2

=(OA+AC)

2

+BC

2

. . . . . . ( i )

Intriangle ABC,

cosθ=

AB

AC

or , AC = AB cosθ

or , AC = OD cosθ

= Q cosθ [ AB = OD = Q ]

Also,

cosθ=

AB

BC

or , BC = AB sinθ

or , BC = OD sinθ

= Q sinθ [ AB = OD = Q }

Magnitude of resultant:

Substituting value of AC and BC in ( i ), we get

R

2

=(P+Qcosθ)

2

+(Qsinθ)

2

or , R

2

=P

2

+2PQcosθ+Q

2

cos

2

θ+Q

2

sin

2

θ

or , R

2

=P

2

+2PQcosθ+Q

2

R =

P

2

+2PQcosθ+Q

2

Which is the magnitude of resultant.

Direction of resultant :

Let ϕ be the angle made by resultant R with P . Then,

From triangle OBC,

tanϕ=

OC

BC

=

OA+AC

BC

or , tanϕ=

P+Qcosθ

Qsinθ

ϕ=tan

−1

(P+Qcosθ

Qsinθ )

which is the direction of resultant

Explanation:

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