Question

Result of two vectors of magnitude R and P is magnitude P. If magnitude of P bar is doubled now the angle made by new results with R is

Answer 1

Answer:

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Explanation:

P

+

Q

=

R

Resultant of

P

&

Q

is given as

∣

∣

∣

∣

R

∣

∣

∣

∣

2

=

∣

∣

∣

∣

P

∣

∣

∣

∣

2

+

∣

∣

∣

∣

Q

∣

∣

∣

∣

2

+2

∣

∣

∣

∣

P

∣

∣

∣

∣

∣

∣

∣

∣

Q

∣

∣

∣

∣

cosθ⟶(i)

When Q is doubled, new resultant R

1

is perpendicular to

P

0

⇒(R

1

).

P

=0

(

P

+2

Q

).

P

=0

∣

∣

∣

∣

P

∣

∣

∣

∣

2

+2

∣

∣

∣

∣

P

∣

∣

∣

∣

.

∣

∣

∣

∣

Q

∣

∣

∣

∣

cosθ=0

cosθ=

2

∣

∣

∣

∣

Q

∣

∣

∣

∣

−

∣

∣

∣

∣

P

∣

∣

∣

∣

putting value of cosθ in eqn (i)

∣

∣

∣

∣

R

∣

∣

∣

∣

2

=

∣

∣

∣

∣

P

∣

∣

∣

∣

2

+

∣

∣

∣

∣

Q

∣

∣

∣

∣

2

+2

∣

∣

∣

∣

P

∣

∣

∣

∣

∣

∣

∣

∣

Q

∣

∣

∣

∣

⎣

⎢

⎡

2

∣

∣

∣

∣

Q

∣

∣

∣

∣

−

∣

∣

∣

∣

P

∣

∣

∣

∣

⎦

⎥

⎤

∣

∣

∣

∣

R

∣

∣

∣

∣

2

=

∣

∣

∣

∣

P

∣

∣

∣

∣

2

−

∣

∣

∣

∣

P

∣

∣

∣

∣

2

+

∣

∣

∣

∣

Q

∣

∣

∣

∣

2

∣

∣

∣

∣

R

∣

∣

∣

∣

2

=

∣

∣

∣

∣

Q

∣

∣

∣

∣

2

∣

∣

∣

∣

R

∣

∣

∣

∣

=

∣

∣

∣

∣

Q

∣

∣

∣

∣

∣

∣

∣

∣

R

∣

∣

∣

∣

=

∣

∣

∣

∣

Q

∣

∣

∣

∣

Magnitude of

R

is equal to Q.

solution