Three different vectors all start from, and point away from the Origin. The vect

Question

Three different vectors all start from, and point away from the Origin. The vectors all have the same magnitude. Arrange the vectors such that the magnitude of the vector product of any pair of vectors equals the scalar product of the same pair of vectors.

Note: There are three possible pairings of three different vectors.

Draw a picture of the original vectors along with the appropriate axes that locate the vectors at the Origin.

Write down the original vectors in terms of the components of each vector along each of your axes.

Write down the sum of the three vectors in terms of components of the sum along each of your axes.

Hint: Think in 3D.

Explanation / Answer

vector product is ABsin(theta)

scalar product is ABcos(theta)

both will be equal at angle 45

so all the vectors are at an angle of 45 to each other

let vectors A,B,C

A is || to x axis

B is in plane of xy and at angle of 45 from A anti clockwise

C is at angle of 45 to the plane of xy

A=Ai

B=Bcos45i+Bsin45j

C=Ccos45i+Csin45k

i,j,k are direction unit vectors

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