Vinod Singh and Shweta Pawar Solutions for Chapter: Vectors, Exercise 1: Classical Thinking

For any vectors $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c},$ correct statement is

$[\overrightarrow{a} \overrightarrow{b} \overrightarrow{a}\times \overrightarrow{b}]$ is equal to

If $\overrightarrow{a}$ and $\overrightarrow{b}$ be parallel vectors, then $\left[\overrightarrow{a} \overrightarrow{c} \overrightarrow{b}\right]=$

If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are any three coplanar unit vectors, then

If $\overrightarrow{a}=\frac{11}{2}\hat{\mathit{i}}, \overrightarrow{b}=12\hat{\mathit{j}}$ and $\overrightarrow{c}=\frac{13}{3}\hat{\mathit{k}}$ represents the three co$-$terminus edges of a parallelepiped, then its volume is given by

Three concurrent edges $\overrightarrow{OA}, \overrightarrow{OB}, \overrightarrow{OC}$ of a parallelepiped are represented by three vectors $2\hat{i}+\hat{j}-\hat{k}, \hat{i}+2\hat{j}+3\hat{k}$and $-3\hat{i}-\hat{j}+\hat{k},$ the volume of the solid so formed in cubic unit is

The volume of the tetrahedron whose vertices are $A(1,-1,10), B(-1,-3,7), C(5,-1,1)$ and $D(7,-4,7)$ is

The sum of the three vectors determined by the medians of a triangle directed from the vertices is