Question 18 (2 points)
Determine the value of $k$ such that the planes $2 x-k y+2 k z-4=0$ and $3 x+y-z=2$ are perpendicular.

Answer

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Answer

$ k = \boxed{2} $

Steps

Step 1 ：Find the dot product of the normal vectors of the two planes: (2, -k, 2k) and (3, 1, -1)

Step 2 ：Set the dot product to 0 and solve for k: $ 6 - 3k = 0 $

Step 3 ：$ k = \boxed{2} $