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).`