If |vec"a"| = 10, |vec"b"| = 2 and vec"a".vec"b" = 12, then value of |vec"a" xx vec"b"| is ______.

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KollegeApply · Accepted Answer

If |vec"a"| = 10, |vec"b"| = 2 and vec"a".vec"b" = 12, then value of |vec"a" xx vec"b"| is 16. Explanation: Given that |vec"a"| = 10, |vec"b"| = 2 and vec"a".vec"b" = 12 $\therefore$ `vec"a" . vec"b" = |vec"a"||vec"b"| cos theta $\Rightarrow$ 12 = 10 * 2 * cos theta $\Rightarrow$ cos theta = $\frac{12}{20}$ = $\frac{3}{5}$ $\therefore$ sin theta = sqrt(1 - cos^2theta) $\Rightarrow$ sin theta = sqrt(1 - ($\frac{3}{5}$)^2 $\Rightarrow$ sin theta = sqrt(1 - $\frac{9}{25}$) $\Rightarrow$ sin theta = sqrt($\frac{16}{25}$) $\Rightarrow$ sin theta = $\frac{4}{5}$ Now |vec"a" xx vec"b"| = |vec"a"| |vec"b"| sin theta = 10 * 2 * $\frac{4}{5}$` = 16

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