A vector vec A` when added to the vector ` vec B = 3. 0 hat i+ 4 hat j` yields a resultant vector that is in the positive y-direction and has a magnintude equal to that of ` vec B`. Find the magnitude of ` vec A` .

Explanation

As, ` vec B = 3 hat I + 4 hat j , so ` B = sqrt (3&2 + 4^2 ) = 5`
Let ` vec A= x hat i+ y hat j ,
:. ` vec A+ vec B= ( 3 + x) hat i+ 9 4 + y) hat j` ltbRgt But ` vec A+ vec B = 5 aht j`
:. ` ( 3+ x) aht I + ( 4+ y) jhat j= 5 hat j`
Hence ` 3 + x + 0` or ` ` x=- 3`
and ` 4+ y =5` or ` y=1`
:. ` vec A =- 3 hat i+ hat j`
so ` | vec A| = sqrt ((-3)^2 (1)^2) = sqrt 10` .