# Find the volume of the parallelepiped whose conterminous edges are represented by the vectors

Question:

Find the volume of the parallelepiped whose conterminous edges are represented by the vectors+

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

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

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

iv. $\bar{a}=6 \hat{l}, \bar{b}=2 \hat{\jmath}, \bar{c}=5 \hat{k}$

Solution: