Q) A plane passes through points $(1,1,-2)$ and $(3,2,0)$ and is parallel to vectors $i+2j+k$ and $2i-j-2k.$ Find the vector equation of plane in scalar product form.
So, what I've done so far is take the cross product of the two vectors and take that as the direction vector of the plane. Then, i used the dot product of one of the given points and the direction vector of the plane to form the equation. This is my answer:
$$r.(-5i+4j-5k) = 9$$
However, this answer was wrong compared to the textbook answer. Any help is greatly appreciated.
Best Answer
$$ (i+2j+k) \times (2i-j-2k) = (-3i+4j-5k). $$ It seems you wrote $(-5i+4j-5k)$ instead of the correct cross product.