Show that the planes a x + a z = c and b x −...

Brenton Dixon

Brenton Dixon

Answered

2022-07-20

Show that the planes a x + a z = c and b x b y = d, where a , b , c , d R , a , b 0, always form an angle of π / 3 = 60

Answer & Explanation

Damarion Pierce

Damarion Pierce

Expert

2022-07-21Added 11 answers

The main idea would be to note that the angle between planes is the same as the angle between their normal vectors, which are ( a , 0 , a ) and ( b , b , 0 )
Now for any vectors x , y , the key to the angle θ x y between them is in their dot product, which can be computed coordinate-wise, but is also given by
x y = | x | | y | cos θ x y .
You have x = ( a , 0 , a ) , y = ( b , b , 0 )

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