MATH 2400 Quiz: Quiz3Solutions

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31 Jan 2019
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Math 2400: find the equation of the plane that goes through the origin, and is perpendic- ular to the planes. Let ~n1 = h2, 0, 1i , ~n2 = h3, 1, 2i, which are normal vectors to the two given planes. A plane perpendicular to the two given planes will have a normal vector perpendicular to ~n1 and ~n2, which can be found by the cross product: Since the plane goes through the origin, the equation is x + 7y + 2z = 0: find a vector ~w that bisects the smaller of the two angles formed by 3 i 4 j and 12 i + 5 j. First, rescale the vectors so that they are unit vectors: ~u = (cid:28)3. Letting ~w = ~u + ~v = (cid:10) 99 isosceles triangle de ned be ~u, ~v, ~w, that ~w bisects the angle. Alternatively, we can start with ~w as an arbitrary vector ha, bi.