Find a vector v for which the parallelogram formed by v and w = <2, 2, -1> has area equal to 6.

Expert Answers
tiburtius eNotes educator| Certified Educator

You can calculate this by using cross product.


Let's first calculate cross product



Now we calculate norm of that vactor which needs to be equal to 6.




So any vector `v=(v_1,v_2,v_3)` which satisfies the above equation will form parallelogram of area 6 with vector `w.`  Obviously there are infinitely many solutions. One is e.g. if you put `v_1=v_2=0` , your equation becomes


Hence two solutions (out of infinitely many) are `(0,0,3/sqrt2)` and `(0,0,-3/sqrt2).`