Question

Find the area of parallelogram whose adjacent sides are given by vectors

Answer 1

Let a→=i^−j^+3k^

b→=2i^−7j^+k^

Area of the parallelogram is the cross product of its adjacent sides.

Here AB−→−=a→=i^−j^+3k^

AD−→−=b→=2i^−7j^+k^

Therefore area of the parallelogram is given by |a→×b→|

Step 2:

Let us determine a→×b→.

a→×b→=∣∣∣∣∣i^a1b1j^a2b2k^a3b3∣∣∣∣∣

a→×b→=∣∣∣∣∣i^12j^−1−7k^31∣∣∣∣∣

=i^(−1×1−3×−7)−j^(1×1−3×2)+k^(1×−7−2×−1)

=i^(−1+21)−j^(1−6)+k^(−7+2)

=20i^+5j^−5k^

Step 3:

Area of the parallelogram = |a→×b→|

|a→×b→|=202+52+(−5)2−−−−−−−−−−−−−√

=400+25+25−−−−−−−−−−−√

=450−−−√

=152–√

Therefore area of the parallelogram is 152–√sq.units.