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

$k = 2$

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: $6 - 3 k = 0$

Step 3 ： $k = 2$