Answer:
X has the form Ai + 16j, where A is some number greater than -12.
Then X + Y = (A+12)i, where A+12 > 0. So, X + Y lies along the positive x-axis.
Since we want the magnitude of X + Y to be the same as the magnitude of X, we have A+12 = √(A2+256)
Squaring both sides, we obtain A2 + 24A + 144 = A2 + 256
So, 24A + 144 = 256
24A = 112
A = 112/24 = 14/3
X = (14/3)i + 16j
The magnitude of X is √[(14/3)2 + 162] = 50/3
Step-by-step explanation:
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