Question

Find the angle between the planes 2x-3y+z=0 and x+2y+7z-3=0

Comments

As We Know Angle Between Planes Is Angle Between The Normals.
Let A = 2x - 3y + z =0 B = x + 2y + 7z -3 = 0
Normal Of A Is :- 2i - 3j +k
Normal Of B Is :- i + 2j + 7k Dot Product Of A And B (F) :- (2)(1) + (-3)(2) + (1)(7) = 2-6+7 = 1 Magnitude Of Normal A (G) :- √14 Magnitude Of Normal B (H) :- √54 G × H × Cos∆ = F
√14 × √54 × Cos∆ = 1
Cos∆ = 1 ÷√14 × √54
∆ = Cos–¹( Value Of Cos∆ )

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