List of top Mathematics Questions on Vectors asked in Bihar Board XII

Find the distance between the planes \[ x - 2y + 2z = 6 \quad \text{and} \quad 3x - 6y + 6z = 2. \]

Find the equation of the plane whose intercepts on the axes \(x, y, z\) are respectively \(2, 3\), and \(-4\).

Find the value of \(p\) so that the lines \[ \frac{x-1}{2} = \frac{y-2}{3} = \frac{z+17}{p} \quad \text{and} \quad \frac{x+4}{2} = \frac{y+9}{2} = \frac{z-1}{2} \] are mutually perpendicular.

Find the angle between the vectors \[ \mathbf{A} = 5\vec{i} + 3\vec{j} + 4\vec{k} \quad \text{and} \quad \mathbf{B} = 6\vec{i} - 8\vec{j} - \vec{k}. \]

Given that \[ |\vec{a} + \vec{b}| = |\vec{a} - \vec{b}| \] which of the following is true?

The projection of the vector \[ \vec{a} = \hat{i} - 2\hat{j} + \hat{k} \] on the vector \[ \vec{b} = 4\hat{i} - 4\hat{j} + 7\hat{k} \] is:

Find the value of: \[ \vec{a} \times (\vec{b} + \vec{c}) + \vec{b} \times (\vec{c} + \vec{a}) + \vec{c} \times (\vec{a} + \vec{b}) \]

Find the value of the scalar triple product: \[ \hat{i} \cdot (\hat{j} \times \hat{k}) \]

If \[ \vec{a} = \hat{i} + \hat{j} + 2\hat{k}, \] then the corresponding unit vector \( \hat{a} \) in the direction of \( \vec{a} \) is:

If \[ \vec{a} = 3\hat{i} + \hat{j} - 2\hat{k} \quad \text{and} \quad \vec{b} = \hat{i} + \lambda \hat{j} - 3\hat{k} \] are perpendicular to each other, then the value of \( \lambda \) is:

The angle between the vectors \[ \vec{a} = 2\hat{i} - 3\hat{j} + 2\hat{k} \quad \text{and} \quad \vec{b} = \hat{i} + 4\hat{j} + 5\hat{k} \] is:

Find the dot product of the vectors: \[ (4\hat{i} + 3\hat{j} + 3\hat{k}) \cdot (6\hat{i} - 4\hat{j} + \hat{k}) \]

Find the cross product of the vectors: \[ \left( \hat{i} + 3\hat{j} - 2\hat{k} \right) \times \left( -\hat{i} + 3\hat{k} \right) \]

Find the magnitude of the vector: \[ \left| \hat{i} - \hat{j} - \hat{k} \right| \]

Find the dot product of the unit vectors: \[ \hat{j} \cdot \hat{j} \]

Find the cross product of the unit vectors: \[ \hat{k} \times \hat{j} \]