List of top Mathematics Questions on Vector Algebra asked in WBJEE

The value of 'a' for which the scaler triple product formed by the vectors \(\vec\alpha=\hat{i}+a\hat{j}+\hat{k}\),  \(\vec{\beta}=\hat{j}+a\hat{k}\)  and  \(\vec{\gamma}=a\hat{i}+\hat{k}\)  is maximum, is

If the volume of the parallelopiped with \(\vec a\times \vec b\), \(\vec b\times \vec c\)  and  \(\vec c\times \vec a\) as coterminous edges is 9 cu. units,then the volume of the parallelopiped with (\(\vec a\times \vec b\))×(\(\vec b\times \vec c\)), (\(\vec b\times \vec c\))×(\(\vec c\times \vec a\)) and (\(\vec c\times \vec a\))×(\(\vec a\times \vec b\)) as coterminous edges is

For any vector $x$, where $\hat{ i }, \hat{ j }, \hat{ k }$ have their usual meanings the value of $( x \times \hat{ i })^{2}+( x \times \hat{ j })^{2}+( x \times \hat{ k })^{2}$ where $\hat{ i }, \hat{ j }, \mathbf { k }$ have their usual meanings, is equal to

For non-zero vectors $\vec{a} $ and $\vec{b} $ if $\left|\vec{a}+\vec{b}\right|

If the four points with position vectors $-2\hat{i}+\hat{j}+k, \hat{i} +\hat{j}+\hat{k}, \hat{j}-\hat{k}, $ and $\lambda\hat{j}+\hat{k}$ are coplanar, then $\lambda=$