Question

If $a=2i-3j+k,b=-i+k,c=2j-k,$ find the area of the parallelogram having diagonals a+band b+c.

• A. $Area=\frac{1}{4}\sqrt{21}.$
• B. $Area=\frac{1}{4}\sqrt{19}.$
• C. $Area=\frac{1}{2}\sqrt{19}.$
• D. $Area=\frac{1}{2}\sqrt{21}.$

Answer 1

Answer: (D)

$Area=\frac{1}{2}\sqrt{21}.$

Let $d_1=a+b=i-3j+2k,d_2=b+c=-i+2j$
Now $d_1\times d_2=\left|\begin{array}{ccc}i& j& k\\ 1& -3& 2\\ -1& 2& 0\end{array}\right|=-4i-2j-k$
Hence area of parallelogram is $=\frac{1}{2}|d_1\times d_2|=\frac{1}{2}\sqrt{21}$