Answer:
\[|\vec{a}-\vec{b}{{|}^{2}}-{{(|\vec{a}|+|\vec{b}|)}^{2}}\] \[=|\vec{a}{{|}^{2}}+|\vec{b}{{|}^{2}}-2|\vec{a}||\vec{b}|\cos \theta -|\vec{a}{{|}^{2}}\] \[-|\vec{b}{{|}^{2}}-2\] \[|\vec{a}||\vec{b}|\] \[=-4|\vec{a}\text{ }\!\!|\!\!\text{ }\!\!|\!\!\text{ }\vec{b}|{{\cos }^{2}}\frac{\theta }{2}\]= a negative quantity Hence \[|\vec{a}-\vec{b}|\le |\vec{a}|+|\vec{b}|\].
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