I am lost on this question - if I need to find the angle of intersection between the planes, I would assume I can just find the angle between their two normal vectors using the dot product formula
A dot B = ||A||||B||cos(theta), where A and B are the two normal vectors to the planes. I plotted both planes in Wolfram and visually it seems like that should give the right answer. I also found an answer on MathExchange that uses this method to solve a similar problem (and defines the angle of intersection between two planes as being the angle between the normal vectors). However, no matter the angle I find (obtuse or acute) with this method, the angle is reported as being incorrect
How should I go about doing this if this is not the correct method?
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You aren't doing anything wrong, except you let webwork fool you into thinking that the normal vector of the first plane is <1,-4,1>. It's not. Notice that the coefficient of x is -4, while that of y is 1? The coefficient of x goes in the x-position and of y goes in the y-position. This means that the normal vector is <-4,1,1>.
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