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

< Science:Math Exam Resources | Courses/MATH152 | April 2011 | Question A 16(Redirected from Science:Math Exam Resources/Courses/MATH152/April 2011/Question A16/Solution 1)

Jump to navigation
Jump to search
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