Question

If $\left[\overline{a}\overline{b}\overline{c}\right]=5$, then the volume of the parellelepiped with $\overline{a}+2\overline{b},2\overline{b}+\overline{c}$ and $\overline{c}+2\overline{a}$ as coterminus edges is

• A. $10$cu. Units
• B. $20$cu. Units
• C. $30$cu. Units
• D. $25$cu. Units

Answer 1

The correct option is C $30$cu. Units

given $\to \left[abc\right]=5$

(volumes of parallelopiped) $=[a+2b,2b+c,c+2a]$

$V=[a+2b,c-a,c+2a]$

$V=[a+2b,3a,c+2a]$

$V=3[a+2b,a,c+2a]$

$V=3[2b,a,c]$

$=6[b,a,c]$

$V=6\left(5\right)$

$V=30cu.units$