When two planes intersect, the angle between the planes is defined as the non-obtuse angle between their normals. If N_(1) and N_(2) are the normals of two intersecting planes, the angle theta between these planes is given by cos( theta )=(|N_(1)*N_(2)|)/(||N_(1)||||N_(2)||),0

Question

When two planes intersect, the angle between the planes is defined as the non-obtuse angle between their normals. If

N_(1)

and

N_(2)

are the normals of two intersecting planes, the angle

\theta

between these planes is given by

cos(\theta )=(|N_(1)*N_(2)|)/(||N_(1)||||N_(2)||),0<=\theta <=(\pi )/(2)

Find the angle

\theta

between two intersecting planes

3x-2y+z=7

and

2x-3y+4z=7

. (Express numbers in exact form. Use symbolic notation and fractions where needed.)

\theta =

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