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

If $\vec{c} = 5\vec{a} + 6\vec{b}$ and $3\vec{c} = \vec{a} - 4\vec{b}$ then}
If $\vec{c} = 5\vec{a} + 6\vec{b}$ and $3\vec{c} = \vec{a} - 4\vec{b}$ then}
If $\vec{c} = 5\vec{a} + 6\vec{b}$ and $3\vec{c} = \vec{a} - 4\vec{b}$ then}
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:

If $\vec{r} = -4\hat{i} - 6\hat{j} - 2\hat{k}$ is a linear combination of the vectors $\vec{a} = -\hat{i} + 4\hat{j} + 3\hat{k}$ and $\vec{b} = -8\hat{i} - \hat{j} + 3\hat{k}$, then
In a quadrilateral PQRS, M and N are mid-points of the sides PQ and RS respectively. If $\overline{PS} + \overline{QR} = t\overline{MN}$, then $t =$