Question

I need help to solve the question. what can be the answer and how do we justify?

Answer 1

let A=xi+yj
when added to B...
new vector becomes
$c = (x + 3)i + (y + 4)j$
...
it is in y axis hence "i" cap term =0
$x + 3 = 0 \\ x = - 3...............(1)$

$c = (y +4)j$

magnitude of this vector is equal to magnitude of b
$= \sqrt{ {3}^{2} + {4}^{2} } = 5$
so magnitude of C =5
$\sqrt{ {0}^{2} + {(y + 4)}^{2} } = 5 \\ y + 4= 5 \\ y = 1......(2)$
now vector A (xi+yj)becomes
$a = - 3i + 1j$


from (1) and (2)

mag|A|
$= \sqrt{ {3}^{2} + {1}^{2} } \\ = \sqrt{10}$


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