Question

The area of the parallelogram whose adjacent sides are 2i - 3k and 4j + 2k is

• A. $2\sqrt{\left(14\right)}$
• B. $4\sqrt{\left(14\right)}$
• C. $16\sqrt{\left(14\right)}$
• D. $\sqrt{\left(14\right)}$

Answer 1

The correct option is B $4\sqrt{\left(14\right)}$

Let $a=2i-3k,b=4j+2k$
Thus $a\times b=\left|\begin{array}{ccc}i& j& k\\ 2& 0& -3\\ 0& 4& 2\end{array}\right|=12i-4j+8k=4(3i-j+2k)$
Hence area of parallelogram $=|a\times b|=4\sqrt{14}$