Find the area of the parallelogram that has the vectors as adjacent sides.

u = i+2j+2k v = i+k

I know that I have to use (-2,-2,2)

sqrt (1-2)^2 + (2+2)^2 + (2-2)^2 =
sqrt17

Area = sqrt 17. Is this correct?

yes

To find the area of a parallelogram given the vectors as adjacent sides, you can use the cross product of the vectors and take its magnitude. Let's go through the steps to find the area using the given vectors u = i + 2j + 2k and v = i + k.

1. Take the cross product of the two vectors:
u x v = (2 * 1 - 2 * 1)i + (2 * 1 - 2 * 1)j + ((1 * 2) - (1 * 2))k
= 0i + 0j + 0k
= 0

2. Calculate the magnitude of the cross product:
|u x v| = |0| = 0

The magnitude of the cross product is zero, which means that the two vectors u and v are parallel or anti-parallel, and the area of the parallelogram is zero. This implies that either the vectors don't form a parallelogram or they are collinear.

Therefore, the given vectors u = i + 2j + 2k and v = i + k do not form a parallelogram. It seems there might be a mistake in the vectors provided.