Let u = (1,0,2) , v = (0,-1,2) and w = (2,1,0). compute (i) the area of the parallelogram bounded by u and v (5) (ii) the equation of the plane parallel to v and w pass through the tip of u

Answers: 

(i) 3
(ii) 
 
Explanation: 

(i) The area of the parallelogram bounded by vectors u and v is given by:



Note that if ,



Thus, the area of the parallelogram formed by vectors u and v is calculated as



Hence, the area of the parallelogram is 3.

(ii) To obtain the equation of the plane, we must get its normal vector and a point in the plane.

As calculated in (i), the normal vector to the plane is  because the plane is parallel to vectors v and w. Note that if ,



Thus, a normal vector to the plane is .

To get a point in the plane, note that vector u can be represented by any pairs of points. So, we can take (0, 0, 0) to be the starting point of vector u. Since , the tip of vector u is . Because the plane passes thru the tip of vector u, a point in the plane has coordinates . 

So for any point  in the plane, the equation is given by



Where n is the normal vector to the plane.

Since , the equation becomes