Three concurrent edges OA, OB, OC of a parallelopiped are represe… - Vidyadip

MCQ

Three concurrent edges $ OA, OB, OC$ of a parallelopiped are represented by three vectors $2i + j - k,\,\,i + 2j + 3k$ and $ - 3i - j + k,$ the volume of the solid so formed in cubic unit is

✓
$5$
B
$6$
C
$7$
D
$8$

✓

Answer

Correct option: A.

$5$

a
(a) Vol. of parallelopiped

$ = \left| {\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}} \right| = \left| {\begin{array}{*{20}{c}}2&1&{ - 1}\\1&2&3\\{ - 3}&{ - 1}&1\end{array}} \right|$

$ = 2(5) - 1(1 + 9) - 1(5) = \,| - 5|\, = 5$ cubic unit.

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