List of top Mathematics Questions on Vector Algebra asked in Bihar Board XII

Which of the following is an objective function?
Find the dot product of \( (i - 2j + 5k) \cdot (-2i + 4j + 2k) \).
Evaluate the expression \( (i \times j) + (i \times i) \).
Find the value of \( (k \times j) \cdot i \).
Evaluate the following expression: \[ \mathbf{i} \cdot \mathbf{i} + \mathbf{i} \cdot \mathbf{j} + \mathbf{j} \cdot \mathbf{j} + \mathbf{j} \cdot \mathbf{k} + \mathbf{k} \cdot \mathbf{k} \]
Find the dot product of the vectors \[ (11\mathbf{i} + \mathbf{j} + \mathbf{k}) \cdot (\mathbf{i} + \mathbf{j} + 11\mathbf{k}). \]
Find the magnitude of the vector \[ \left| \mathbf{i} - \mathbf{j} - 3 \mathbf{k} \right|. \]
Find the square of the vector \[ (4\mathbf{i} + 3\mathbf{j})^2. \]
Find the dot product of the vectors \[ (7\mathbf{i} - 8\mathbf{j} + 9\mathbf{k}) \cdot (\mathbf{i} - \mathbf{j} + \mathbf{k}). \]
Evaluate: \[ (\vec{i} - 3\vec{j} + 4\vec{k}) \cdot \big[(2\vec{i} - \vec{j}) \times (\vec{j} + \vec{k})\big]. \]
If \(\vec{a} = \vec{i} - \vec{j} + \vec{k}\) and \(\vec{b} = 2\vec{i} + \vec{j} + 3\vec{k}\), then find the value of \(|\vec{a} + \vec{b}|\).
Find the direction cosines of the vector \(3\vec{i} - 4\vec{j} + 12\vec{k}\).
The direction cosines of the \( z \)-axis are:
\(\left\lVert 3\vec i-4\vec j-5\vec k\right\rVert =\) ?
Evaluate \((\vec j-2\vec i)\cdot(\vec k+3\vec i-\vec j)\).
Compute \((2\vec i-3\vec j)\cdot(\vec i+\vec k)\).
\(\vec i\cdot\vec i=\) ?
\(\vec j\times\vec i=\) ?

\(3\vec{k}\cdot(13\vec{i}-7\vec{k})=\) ?

\(\big(3\vec{i}-4\vec{k}\big)^{2}=\) ?

The unit vector in the direction of \(3\vec{i}-9\vec{j}\) is

\((\vec{i}-\vec{j}+\vec{k})\cdot(7\vec{i}-8\vec{j}+9\vec{k})=\) ?

\((11\vec{i}-7\vec{j}-\vec{k})\cdot(8\vec{i}-\vec{j}-5\vec{k})=\) ?

\((3\vec{k}-7\vec{i})\times 2\vec{k}=\) ?

\(\ \left|\ \vec{i}-2\vec{j}+2\vec{k}\ \right|=\) ?