Question

The sides ,of a paralIelogram are represented by vectors $p = 5 \hat i - 4 \hat j + 3 \hat k \, and \, q = 3 \hat i + 2 \hat j - \hat k$. Then the area of the parallelogram is

• A. $\sqrt{684}$ unit
• B. $\sqrt{72}$ unit
• C. 171 unit
• D. 72 unit
• E. $\sqrt{191}$ unit

Answer 1

Answer: (A)

Area of a parallelogram is
$ = |a \times b|$
where a and b arc diagonals.
Given, $20mm a = p = 5 \hat i - 4 \hat j + 3 \hat k$
$ b = q = 3 \hat i + 2 \hat j - \hat k$
$\therefore a \times b = \begin{vmatrix} \hat i & \hat j & \hat k \\ 5 & -4 & 3\\ 3 & 2 & -1\\ \end{vmatrix}$
$a \times b = \hat i (4 - 6) - \hat j (-5 - 9) + \hat k (10 + 12)$
$ a \times b = -2 \hat i + 14 \hat j + 22 \hat k$
$ |a \times b| = \sqrt{(2)^2 + (14)^2 + (22)^2} = \sqrt{684}$