1 Find $[ \vec a\: \: \vec b \: \: \vec c ]\: \: i\! f \: \: \vec a = \hat i - 2 \hat j + 3 \hat k, \vec b = 2 \hat i - 3 \hat j + \hat k \: \:and \: \: \vec c = 3 \hat i + \hat j - 2 \hat k$

P Pankaj Sanodiya

Given,

$\vec a = \hat i - 2 \hat j + 3 \hat k, \vec b = 2 \hat i - 3 \hat j + \hat k \: \:and \: \: \vec c = 3 \hat i + \hat j - 2 \hat k$

$[ \vec a\: \: \vec b \: \: \vec c ]=$

$\\=\begin{vmatrix} 1 &-2 &3 \\ 2& -3& 1\\ 3&1 &-2 \end{vmatrix}\\=1(6-1)+2(-4-3)+3(2+9)\\=5-14+33\\=24$

Hence the value of $[ \vec a\: \: \vec b \: \: \vec c ]$ is 24.

Exams
Articles
Questions