If a force acting on a particle is represented by a vector \(\vec{a}\)=5\(\hat{i}\)-10\(\hat{j}\), then find the angle made by the vector with Y axis.If another force \(\vec{b}\)=10\(\hat{i}\)+5\(\hat{j}\) also acts on the same particle simultaneously then, find their resultant vector and angle made with X axis.

\(\vec{a}\)=5\(\hat{i}\)-10\(\hat{j}\)

So the magnitude of the vector \(\vec{a}\),

|a|=\(\sqrt{5^{2} + (-10)^{2}}\) = \(\sqrt{25+100}\) = \(\sqrt{125}\) =5\(\sqrt{5}\)