Question

The sides ,of a paralIelogram are represented by vectors $p=5\hat{i}-4\hat{j}+3\hat{k}andq=3\hat{i}+2\hat{j}-\hat{k}$. 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, $20mma=p=5\hat{i}-4\hat{j}+3\hat{k}$
$b=q=3\hat{i}+2\hat{j}-\hat{k}$
$\therefore a\times b=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 5& -4& 3\\ 3& 2& -1\end{array}\right|$
$a\times b=\hat{i}(4-6)-\hat{j}(-5-9)+\hat{k}(10+12)$
$a\times b=-2\hat{i}+14\hat{j}+22\hat{k}$
$|a\times b|=\sqrt{(2{)}^2+(14{)}^2+(22{)}^2}=\sqrt{684}$