Science:Math Exam Resources/Courses/MATH152/April 2011/Question A 16/Solution 1

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The first plane

has normal n=[0,1,-1] (just the coefficients on x,y,z). The second plane

has normal n=[2,1,1]. Let's call the direction our line has v. Notice that since v is an intersection of the two planes then by definition it is on plane 1 and plane 2. Therefore

Therefore we seek v so that it is orthogonal to both normal vectors. The cross product, by definition, provides this direction. Therefore,

We want this to have length 1 and so we see that

Therefore we get that the unit norm vector, is