Mathematics - Vector Question with Solution | TestHub

If$h$is the altitude of a parallelopiped determined by the vectors$\hat{a}, \hat{b}, \hat{c}$and the base is taken to be the parallelogram determined by$\hat{a}$and$\hat{b}$where$\hat{a}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \hat{b}=2\hat{\mathrm{i}}+4\hat{\mathrm{j}}-\hat{\mathrm{k}}$and$\hat{c}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+3\hat{\mathrm{k}},$then the value of$19h^2$is