List of top Mathematics Questions on Vectors asked in AP EAMCET

If the vectors \( a\hat{i} + \hat{j} + 3\hat{k} \), \( 4\hat{i} + 5\hat{j} + \hat{k} \), and \( 4\hat{i} + 2\hat{j} + 6\hat{k} \) are coplanar, then \( a \) is:
If \( P = (0,1,2) \), \( Q = (4,-2,-1) \) and \( O = (0,0,0) \), then \( \angle POQ \) is:
In \( \triangle PQR \), \((4\overline{i} + 3\overline{j} + 6\overline{k} )\) and \((3\overline{i} + \overline{j} + 3\overline{k} )\) are the position vectors of the vertices P, Q, R respectively. Then the position vector of the point of intersection of the angle bisector of \( P \) with \( QR \).
The values of \( x \) for which the angle between the vectors \[ \mathbf{a} = x\hat{i} + 2\hat{j} + \hat{k}, \quad \mathbf{b} = -\hat{i} + 2\hat{j} + x\hat{k} \] is obtuse lie in the interval:
Let \( |\mathbf{a}| = 2, |\mathbf{b}| = 3 \) and the angle between \( \mathbf{a} \) and \( \mathbf{b} \) be \( \frac{\pi}{3} \). If a parallelogram is constructed with adjacent sides \( 2\mathbf{a} + 3\mathbf{b} \) and \( \mathbf{a} - \mathbf{b} \), then its shorter diagonal is of length:
If \( \vec{f} = i + j + k \) and \( \vec{g} = 2i - j + 3k \), then the projection vector of \( \vec{f} \) on \( \vec{g} \) is:
Let \( \mathbf{a} = 3\hat{i} + 4\hat{j} - 5\hat{k} \), \( \mathbf{b} = 2\hat{i} + \hat{j} - 2\hat{k} \). The projection of the sum of the vectors \( \mathbf{a}, \mathbf{b} \) on the vector perpendicular to the plane of \( \mathbf{a}, \mathbf{b} \) is:
If \( \hat{i} - \hat{j} - \hat{k} \), \( \hat{i} + \hat{j} + \hat{k} \), \( \hat{i} + \hat{j} + 2\hat{k} \), and \( 2\hat{i} + \hat{j} \) are the vertices of a tetrahedron, then its volume is: