If a and b are two vectors, then (a b)^2 equals - Vidyadip

MCQ

If $ a $ and $b$ are two vectors, then ${(a \times b)^2}$ equals

A
$\left| {\,\begin{array}{*{20}{c}}{a\,\,.\,\,b}&{a\,\,.\,\,a}\\{b\,\,.\,\,b}&{b\,\,.\,\,a}\end{array}\,} \right|$
✓
$\left| {\,\begin{array}{*{20}{c}}{a\,\,.\,\,a}&{a\,\,.\,\,b}\\{b\,\,.\,\,a}&{b\,\,.\,\,b}\end{array}\,} \right|$
C
$\left| {\,\begin{array}{*{20}{c}}{a\,\,.\,\,b}\\{b\,\,.\,\,a}\end{array}\,} \right|$
D
None of these

✓

Answer

Correct option: B.

$\left| {\,\begin{array}{*{20}{c}}{a\,\,.\,\,a}&{a\,\,.\,\,b}\\{b\,\,.\,\,a}&{b\,\,.\,\,b}\end{array}\,} \right|$

b
(b) ${(a \times b)^2} = {a^2}{b^2} - {(a\,.\,b)^2} = \left| {\,\begin{array}{*{20}{c}}{a\,.\,a}&{a\,.\,b}\\{a\,.\,b}&{b\,.\,b}\end{array}\,} \right|.$

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