Question

If A and B are vectors such as A+3b=-3i+j and A-B=i-2j find A and B​

Answer 1

Solve by elimination.

`(\vec A + 3\, \vec B) - (\vec A - \vec B) = (-3\,\vec\imath + \vec\jmath) - (\vec\imath - 2\,\vec\jmath)`

`\implies 4\,\vec B = -4\,\vec\imath + 3\,\vec\jmath \implies \boxed{\vec B = -\vec\imath + \frac34\,\vec\jmath}`

`\implies \vec A = \vec\imath - 2\,\vec\jmath + \vec B`

`\implies \boxed{\vec A = -\frac54 \,\vec\jmath}`