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Question

A vector X is added to vector Y = 12i -16j. The resultant vector lies along the positive x axis and has the same magnitude as X. What is the magnitude of X?

Answer 1

Let X = Ai + Bj

 

Then X+Y = (A+12)i + (B-16)j

 

Since X+Y lies along he positive x-axis, A+12 is positive and B-16 = 0

 

Therefore, B = 16.  So, X = Ai + 16j and X+Y = (A+12)i

 

Since X+Y and X have the same magnitude, we have √[(A+12)²+0²] = √[A²+16²]

 

Simplifying, we get A²+24A+144 = A²+256

 

                                  24A + 144 = 256

 

                                            24A = 112

 

                                                A = 112/24 = 14/3

 

So, X = (14/3)i + 16j

 

Magnitude of X is √[(14/3)²+16²] = 50/3 (approximately 16.7)