The angle between two planes is the smallest angle ( heta ) between the normal vectors of the planes, where the directions of the normal vectors are chosen so that ( 0 leq heta leq frac{pi}{2} ). Find the angle between the planes ( 4 x+6 y-z=0 ) and ( -5 x+3 y+2 z=0 ). The angle between the planes is (Do not round until the final answer. Then round to the nearest degree as needed.)
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The normal vector of a plane is given by the coefficients of x, y, and z in the equation of the plane. So, for the plane 4x + 6y - z = 0, the normal vector is (4, 6, -1). For the plane -5x + 3y + 2z = 0, the normal vector is (-5, 3, 2). Show more…
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