Vinod Singh and Shweta Pawar Solutions for Chapter: Vectors, Exercise 2: Critical Thinking

If the volume of the parallelepiped with coterminous edges $-p\hat{i}+5k, \hat{i}-\hat{j}+q\hat{k}$ and $3 \hat{i}-5 \hat{j}$ is $8,$ then

If the volume of tetrahedron where vertices $\left(1,2,0\right), \left(2,0,4\right), \left(-1,2,0\right)$ and $\left(-1,1,\lambda \right)$ is $\frac{2}{3}$ cu. unit, then find the value of $\lambda$.

If $D$ is the mid-point of side $AB$ of $\Delta ABC$, then $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{AC}=$

The vectors $\overrightarrow{AB}=3\hat{i}+4\hat{k}$ and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$ are sides of a triangle $ABC$. The length of the median through $A$ is

If $G$ and $G^{\text{'}}$ are the centroids of the triangles $A B C$ and $A^{\text{'}} B^{\text{'}} C^{\text{'}},$ then $\overrightarrow{AA\text{'}}+\overrightarrow{BB\text{'}}+\overrightarrow{CC\text{'}}$ is equal to

If $O$ is the circumcentre and $H$ is the orthocentre of the triangle $ABC\mathit{,}$ then $\overrightarrow{HA}+\overrightarrow{HB}+\overrightarrow{HC}=$

If $A\left(-3,-2,0\right), B\left(3,-3,1\right)$ and $C\left(5,0,2\right)$ are three successive vertices of parallelogram $ABCD,$ then its fourth vertex $D$ is

In a trapezium $ABCD$, if the vector $\overrightarrow{BC}=\lambda \overrightarrow{AD},\overrightarrow{P}=\overrightarrow{AC}+\overrightarrow{BD}$ is collinear with $\overrightarrow{AD}$ and $\overrightarrow{P}=\mu \overrightarrow{AD},$ then