Question

if$\overline{a}=\hat{i}+\hat{j}+\hat{k},\overline{b}=\hat{i}-\hat{j}+\hat{k},\overline{c}=\hat{i}+\widehat{2j}-\hat{k}$ then the value of $\left|\begin{array}{ccc}\overline{a}\cdot \overline{a}& \overline{a}\cdot \overline{b}& \overline{a}\cdot \overline{c}\\ \overline{b}\cdot \overline{a}& \overline{b}\cdot \overline{b}& \overline{b}\cdot \overline{c}\\ \overline{c}\cdot \overline{a}& \overline{c}\cdot \overline{b}& \overline{c}\cdot \overline{c}\end{array}\right|$=

• A. 2
• B. 4
• C. 16
• D. 64

Answer 1

Answer: (C)

16

$\left|\begin{array}{ccc}\overline{a}\cdot \overline{a}& \overline{a}\cdot \overline{b}& \overline{a}\cdot \overline{c}\\ \overline{b}\cdot \overline{a}& \overline{b}\cdot \overline{b}& \overline{b}\cdot \overline{c}\\ \overline{c}\cdot \overline{a}& \overline{c}\cdot \overline{b}& \overline{c}\cdot \overline{c}\end{array}\right|={\left[abc\right]}^2={\left|\begin{array}{ccc}1& 1& 1\\ 1& -1& 1\\ 1& 2& -1\end{array}\right|}^2=16$