R S Aggarwal Solutions for Exercise 2: EXERCISE

Find $\left[\begin{array}{lll}\overrightarrow{a}& \overrightarrow{b}& \overrightarrow{c}\end{array}\right]$, when $\overrightarrow{a}=2\hat{i}-3\hat{j}+4\hat{k}, \overrightarrow{b}=\hat{i}+2\hat{j}-\hat{k}$and $\overrightarrow{c}=3\hat{i}-\hat{j}+2\hat{k}$

Find $\left[\begin{array}{lll}\overrightarrow{a}& \overrightarrow{b}& \overrightarrow{c}\end{array}\right]$, when $\overrightarrow{a}=2\hat{i}-3\hat{j}, \overrightarrow{b}=\hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{c}=3\hat{i}-\hat{k}$.

Find the volume of the parallelepiped (in cubic units) whose conterminous edges are represented by the vectors

$\overrightarrow{a}=-3\hat{i}+7\hat{j}+5\hat{k} ,\overrightarrow{b}=-5\hat{i}+7\hat{j}-3\hat{k}, \overrightarrow{c}=7\hat{i}-5\hat{j}-3\hat{k}$

Find the volume of the parallelepiped (in cubic units) whose conterminous edges are represented by the vectors

$\overrightarrow{a}=\hat{i}-2\hat{j}+3\hat{k}, \overrightarrow{b}=2\hat{i}+\hat{j}-\hat{k}, \overrightarrow{c}=\hat{j}+\hat{k}$

Find the volume of the parallelepiped (in cubic units) whose conterminous edges are represented by the vectors

$\overrightarrow{a}=6\widehat{i,} \overrightarrow{b}=2\hat{j}, \overrightarrow{c}=5\hat{k}$

Find the value of $\lambda$ for which the four points with position vectors $(\hat{i}+2\hat{j}+3\hat{k}),(3\hat{i}-\hat{j}+2\hat{k}),(-2\hat{i}+\lambda \hat{j}+\hat{k})\text{ and }(6\hat{i}-4\hat{j}+2\hat{k})$ are coplanar.

Find the value of $\lambda$ for which the four points with position vectors $(-\hat{j}+\hat{k}),(2\hat{i}-\hat{j}-\hat{k}),(\hat{i}+\lambda \hat{j}+\hat{k})$  and $(3\hat{j}+3\hat{k})$ are coplanar.

Find the value of $\lambda$ for which the points $A(3, 2, 1), B(4, \lambda , 5), C(4, 2, -2) \mathrm{and} D(6, 5, -1)$ are coplanar.