List of top Mathematics Questions on Vectors asked in AP EAMCET

If \( \bar{a} = -4\bar{i} + 2\bar{j} + 4\bar{k} \), \( \bar{b} = \sqrt{2} \bar{i} - \sqrt{2} \bar{j} \) are two vectors, then the angle between the vectors \( 2\bar{a} \) and \( \frac{\bar{b}}{2} \) is:
If \( AB = 2i + 3j - 6k \), \( BC = 6i - 2j + 3k \) are the vectors along two sides of a triangle ABC, then the perimeter of triangle ABC is:
If \( \vec{a} = \hat{i} - \hat{j} + \hat{k} \), \( \vec{b} = \hat{i} + \hat{j} - 2\hat{k} \), \( \vec{c} = 2\hat{i} - 3\hat{j} - 3\hat{k} \), and \( \vec{d} = 2\hat{i} + \hat{j} + \hat{k} \) are four vectors, then \( (\vec{a} \times \vec{c}) \times (\vec{b} \times \vec{d}) = \):
The orthogonal projection vector of \( \bar{a} = 2\bar{i} + 3\bar{j} + 3\bar{k} \) on \( \bar{b} = \bar{i} - 2\bar{j} + \bar{k} \) is:
If the vectors \(a\bar{i} + \bar{j} + \bar{k}\), \(\bar{i} + b\bar{j} + \bar{k}\), \(\bar{i} + \bar{j} + c\bar{k}\) (\(a \ne b \ne c \ne 1\)) are coplanar, then \(\frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c} =\)
If \( \vec{a} = i\hat{i} + j\hat{j} + 3k\hat{k} \), \( \vec{b} = i\hat{i} + 2k\hat{k} \), \( \vec{c} = -3i\hat{i} + 2j\hat{j} + k\hat{k} \) are linearly dependent vectors and the magnitude of \( \vec{a} \) is \( \sqrt{14} \), then if \( \alpha, \beta \) are integers, find \( \alpha + \beta \):
If \( \vec{a}, \vec{b}, \vec{c} \) are 3 vectors such that \( |\vec{a}| = 5, |\vec{b}| = 8, |\vec{c}| = 11 \) and \( \vec{a} + \vec{b} + \vec{c} = 0 \), then the angle between the vectors \( \vec{a} \) and \( \vec{b} \) is:
If \( \vec{i} - 2\vec{j} + 3\vec{k}, 2\vec{i} + 3\vec{j} - \vec{k}, -3\vec{i} - \vec{j} - 2\vec{k} \) are the position vectors of three points A, B, C respectively, then A, B, C: