Question

The resultant of two vectors A and B is Ć. If
the magnitude of B is doubled, the new
resultant vector becomes perpendicular to A,
then the magnitude of C is​

Answer 1

Answer:

C=Magnitude of B

Explanation:

According to the question, A+B=C....(0)

Also, when B is doubled, C becomes perpendicular to A. Let the new magnitude of C be C'

That means A.C' =0 (AC' cos 90 =0)

>(A)(A+2B)=0.......(1)

>(A^2 + 2AB)=0

>|A|=-2AB

To find the magnitude of C, square eq. (0)

>(A+B)^2=|C|

>|A|+|B|+2AB

but 2AB = -|A|. from (1)

which means |C|=|B|

Answer 2

Answer:

B

Explanation:

vect A +vect B = vect C

C²=A²+B²+2ABcostita ............(1)

and tan alpha = Bsin tita/A+B cos tita

when B is doubled resultant is perpendicular to vect A

therefore C²= A²+4B²+4AB cos tita................(2)

from right angle triangle

triangle PSR

4B²=C1²+A²

C1²=4B²-A²

substituting in 2 and solving

A²+2AB cos tita =0 .........(3)

substituting 3 in 1

C=B