List of top Mathematics Questions on Addition of Vectors asked in MHT CET

If \(|\mathbf{a}| = \sqrt{3}, |\mathbf{b}| = 5, |\mathbf{b}||\mathbf{c}| = 10\), the angle between \(\mathbf{b}\) and \(\mathbf{c}\) is \(\pi/3\), and \(\mathbf{a}\) is perpendicular to \(\mathbf{b} \times \mathbf{c}\), then the value of \(|\mathbf{a} \times (\mathbf{b} \times \mathbf{c})|\) is:
The sides of a triangle are \(\sin\alpha\), \(\cos\alpha\), and \(\sqrt{1+\sin\alpha\cos\alpha}\) for some \(0 < \alpha < \frac{\pi}{2}\). Then, the greatest angle of the triangle is: