Given two planes: p1: x+y-z=4 p2: 3x-y+5z=3 The corresponding normal vectors are: n1=<1,1,-1> n2=<3,-1,5> (they are simply the corresponding coefficients of x,y,z)
The line of intersection of p1 and p2 has a direction vector perpendicular to both p1 and p2, thus equal the cross product of n1 and n2, L1=n1 x n2 = i j k 1 1 -1 3 -1 5 =<5-1, -3-5, -1-3> =<4,-8,-4> Since the length of the direction vector does not matter, we simplify the vector to L1=<1,-2,-1>
The required line must pass through the point (-2,3,3). The line therefore has the equation L: (-2,3,3)+t(1,-2,-1) or alternatively, L: x=-2+t, y=3-2t, z=3-t
There are 60 minute per hour. If it is 11:45, it's 25 minutes until 12:10. Once it is 12:10, the next hour (after 50 minutes) would be 1:00. so if you take 11:45 and add the 25 minutes from 3 hours and 25 minutes, it is 12:10 and you are left with 3 hours. 3 hours after 12:10 is 3:10
Letter D because you need to multiply all the letters of the alfabet (36) and multiply 36 by 1000 and then divide the answer by 100 and you get the letter D
