Question in GIKI 2012 Test

Question :

Sum of two vectors A and B is equal to A. Difference of these two vectors is equal to 2A. If A=4 find the MAGNITUDE of vector B.

a)3√2

b)6√2

c)2√6

d)3√6

Question of GIKI test 2012.

Solution:

In terms of rectangular components we can write:
A =√ A²_x + A²_y
B=√ B²_x + B²_y

Given:
A + B = A
it means 
 √( A²_x + A²_y ) +  √( B²_x + B²_y  ) =  4

Squaring Both sides, we get 
A²_x + A²_y  +  B²_x + B²_y   +  2√( A²_x + A²_y )( B²_x + B²_y  ) =  16       (equation i)

Also
A-B = 2A
A-B = 8
√( A²_x + A²_y ) -  √( B²_x + B²_y  ) =  8

Squaring Both sides, we get 
A²_x + A²_y  +  B²_x + B²_y   -  2√( A²_x + A²_y )( B²_x + B²_y  ) =  64      (equation ii)

Adding equation i and ii we get 
2(  A²_x + A²_y  +  B²_x + B²_y  ) =  80
16 + B²_x + B²_y = 40
B²_x + B²_y = 24
B² = 24
B = √24 = √4x6 = 2√6