Question

The resultant of two vectors P and Q is Ř If Q is
doubled then the new resultant vector is perpendicular
to P. Then magnitude of Ř is:​

Answer 1

Answer:

Let the angle between two vectors

P

and

Q

be

α

and their resultant is

R

So we can write

R

2

=

P

2

+

Q

2

+

2

P

Q

cos

α

...

...

[

1

]

When Q is doubled then let the resultant vector be

R

1

, So we can write

R

2

1

=

P

2

+

4

Q

2

+

4

P

Q

cos

α

...

...

[

2

]

Again by the given condition

R

1

is perpendicular to

P

So

4

Q

2

=

P

2

+

R

2

1

...

...

[

3

]

Combining [2] and [3] we get

R

2

1

=

P

2

+

P

2

+

R

2

1

+

4

P

Q

cos

α

⇒

2

P

Q

cos

α

=

−

P

2

...

...

[

4

]

combining [1] and [4] we get

R

2

=

P

2

+

Q

2

−

P

2

⇒

R

=

Q