Discussion Forum

If A,B, C and D are (3,7,4) ,(5,-2,-3) ,(-4,5,6) and (1,2,3) respectively , then the volume of the parallelopiped  with AB, AC and AD as the co-terminus edges, is ........ cubic units

Answer:

Explanation:

 We have

  AB=  $(5-3)\hat{i}+(-2-7)\hat{j}+(3-4)\hat{k}$

  = $2\hat{i}-9\hat{j}-\hat{k}$

AC= $(-4-3)\hat{i}+(5-7)\hat{j}+(6-4)\hat{k}$

= $-7\hat{i}-2\hat{j}+2\hat{k}$

and    AD= $(1-3)\hat{i}+(2-7)\hat{j}+(6-4)\hat{k}$

=  $-2\hat{i}-5\hat{j}-\hat{k}$

$\therefore$   Volume of the parallelopiped with AB,AC and AD on the co-terminus edges

$[(AB$ $AC$ $AD)]=\begin{bmatrix}2 & -9 &-1 \\-7 & -2 &2\\ -2&-5&-1 \end{bmatrix}$

 =|2(2+10)+9(7+4)-1(35-4)|

=|2(12)+9(11)-1(31)|

=|(24+99-31)|

|92|=92 cubic unit