List of top Mathematics Questions on Product of Two Vectors asked in BITSAT

The dot product of a vector with the vectors i+ j-3 k, i+3 j-2 k, 2 i+ j+4 k are 0,5 and 8 respectively. The vector is
Let \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) be non-coplanar unit vectors equally inclined to one another at an acute angle \(\theta\). Then \(|\mathbf{a} \cdot (\mathbf{b} \times \mathbf{c})|\) in terms of \(\theta\) is equal to
The dot product of a vector with the vectors \( \mathbf{i} + \mathbf{j} - 3\mathbf{k} \), \( \mathbf{i} + 3\mathbf{j} - 2\mathbf{k} \) and \( 2\mathbf{i} + \mathbf{j} + 4\mathbf{k} \) are 0, 5 and 8 respectively. The vector is:
If \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) are three unit vectors such that \[ \mathbf{a} + \mathbf{b} + \mathbf{c} = \mathbf{0}, \quad \mathbf{a} \cdot \mathbf{b} = \mathbf{b} \cdot \mathbf{c} = \mathbf{c} \cdot \mathbf{a} \] then the value of \( \mathbf{a} \cdot \mathbf{a} \) is
If \( \mathbf{a} = \mathbf{c} \) and \( \mathbf{b} = \mathbf{a} \times \mathbf{c} \), then the correct statement is:
The unit vector perpendicular to the vectors \( 6i + 2j + 3k \) and \( 3i - 6j - 2k \) is:
If ( a × b)² + ( a · b)² = 676 and | b| = 2, then | a| is equal to
Which one of the following is the unit vector perpendicular to both a = - i + j + k and b = i - j + k?