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Question

Angle between 2 planes ¯r.^n1=d1,¯r.^n2=d2, can always be given by

A
θ=sin1|^n1×^n2|
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B
θ=cos1(^n1.^n2)
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C
θ=sin1|^n1.^n2|
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D
θ=cos1|(^n1.^n2)|
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Solution

The correct option is B θ=cos1(^n1.^n2)
We know the angle between the planes is same as the angle between their normals. Here the normals are ^n1 and ^n2. So we can get the angle between them by dot product,
¯n1.¯n2=cosθ
θ=cos1(^n1.^n2)
One Important thing to notice is that, we will lose information on angle by doing sin1|^n1×^n2| or cos1|^n1.^n2| as it will restrict the value of angle to (0,π2) in case 1 and (π2,π2) in case 2.

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