List of top Mathematics Questions on Addition of Vectors asked in MET

Given vectors \(\vec{a}, \vec{b}, \vec{c}\) are non-collinear and \((\vec{a}+\vec{b})\) is collinear with \((\vec{b}+\vec{c})\) which is collinear with \(\vec{a}\), and \(|\vec{a}|=|\vec{b}|=|\vec{c}|=\sqrt{2}\), find \(|\vec{a}+\vec{b}+\vec{c}|\).

A parallelogram is constructed on vectors \(\vec{a}=3\vec{\alpha}-\vec{\beta},\; \vec{b}=\vec{\alpha}+3\vec{\beta}\). If \(|\vec{\alpha}|=|\vec{\beta}|=2\) and angle between them is \(\pi/3\), find length of a diagonal