Question

A.B=0 and AxC=0 then Ax(BxC)=?​

Answer 1

concept : if two vectors a and b are given such that angle between them is α.

then, dot product of a and b = a.b = |a|.|b|cosα

and cross product of a and b = a × b = |a|.|b|sinα \hat{n}

here \hat{n} represents unit vector along a × b.

given, A.B = 0

it means Vector A makes an angle 90° with vector B and vice-vera.

means , |A|.|B|cosα = 0

or, cosα = 0 = cos90°

or, α = 90°

again, A × C = 0

or, |A|.|C|sinβ \hat{n} = 0

or, sinβ = 0 = sin0°

or, β = 0°

it means, A and C are parallel vectors.

so, we can conclude that angle between B and C is 90°.

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