Question

How to calculate area of parallelogram with vector?

Answer 1

hint towards exams.

Area=|a⃗ ×b⃗ |Area=|a→×b→|

|a⃗ ×b⃗ ||a→×b→|

=

∣∣∣∣i−1−2j0−2k22∣∣∣∣|ijk−102−2−22|

now that we got our tangent vector specified,

∣∣∣0−222∣∣∣i−∣∣∣−1−222∣∣∣j+∣∣∣−1−202∣∣∣k|02−22|i−|−12−22|j+|−10−22|k

∴ your equation of line should be;

4i−(−2+4)j+2k=4i+2j+2k4i−(−2+4)j+2k=4i+2j+2k

Thus Area =

|a⃗ ×b⃗ |=42+22+22−−−−−−−−−−√=24−−√|a→×b→|=42+22+22=24

Hope this helps you.