Vector Solutions to Math Problem: 27V + 8<b>i</b> + 5<b>j</b>

[pyroknife]

I attached the problem along with its answers. The letters in bold indicate a vector, the unbolded Vs are scalars (that's how they defined it in this book.) For the first unbolded one how did they get 27? shouldn't it be the magnitude of the combination of the 2 vectors?

 

[genericusrnme]

from your picture the magnitudes of the two vectors are 12 and 15, 12+15=27
the question is asking for |V_1| + |V_2|, the sum of magnitudes, rather than what I think you mean |V_1 + V_2| which is the magnitude of a sum.

in general |V_1 + V_2| \leq |V_1| + |V_2|

where |V| is the magnitude of V

 

[Pengwuino]

I attached the problem along with its answers. The letters in bold indicate a vector, the unbolded Vs are scalars (that's how they defined it in this book.) For the first unbolded one how did they get 27? shouldn't it be the magnitude of the combination of the 2 vectors?

No, they asked for V_1 + V_2, the sum of the magnitudes of the vectors. What you're suggesting is |\vec{V_1} + \vec{V_2}|, the magnitude of the sum of the vectors.

 

[pyroknife]

Oh thanks guys. That's what I thought it meant from the answer, but I've never seen anything like that before, it's always |V1⃗ +V2⃗