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List of top Physics Questions on Vectors

If the volume of the tetrahedron, whose vertices are \( A(1, 2, 3), B(-3, -1, 1), C(2, 1, 3) \) and \( D(-1, 2, x) \), is \( \frac{11}{6} \) cubic units, then the value of \( x \) is:
If the angle between the line \( 2(x + 1) = y = z \) and the plane \( 2x - y + \sqrt{2} z + 4 = 0 \) is \( \frac{\pi}{6} \), then the value of \( \lambda \) is:
If cos(12/13) + sin(P), then the value of P is:
If \( \mathbf{a} = 2\hat{i} + 2\hat{j} + 3\hat{k}, \mathbf{b} = -\hat{i} + 2\hat{j} + \hat{k} \) and \( \mathbf{c} = 3\hat{i} + \hat{j} \) are the vectors such that \( \mathbf{a} + \lambda \mathbf{b} \) is perpendicular to \( \mathbf{c} \), then the value of \( \lambda \) is:
Approximate value of \( \cos 59^\circ \) is:
Let \( \theta \) be the angle between two vectors \( \vec{A} \) and \( \vec{B} \). If \( \hat{a}_\perp \) is the unit vector perpendicular to \( \vec{A} \), then the direction of \( \vec{B} - \vec{B} \sin \theta \hat{a}_\perp \) is: