Question: Decide an equation for the plane that is perpendicular to the line given by (-1-x)/4=7+y=(7-z)/2 and goes through the point (2,7,-7).
First i set t equal to the line and solved x,y,z and wrote it on paramter form , (x,y,z)=[-1 -7 7]+t*[-4 1 -2]=P1+V, where P1 is a point on the line and V is a vector. I then calculated the vector P1P2=P2-P1=[2 7 -7] - [-1 -7 7]=[3 14 -14]. The normal vector of the plane should be parallel to P1P2 im thinking since the plane is perpendicular to the line, but im having a hard time understand and calculating this. I made one attempt where i set n=P1P2XV (cross product) and got the result 1, but the system says it is the wrong answer. Could someone make an attempt to solve this and explain if you got the time?
Result 1: 42*x+50*y+59*z=21
First i set t equal to the line and solved x,y,z and wrote it on paramter form , (x,y,z)=[-1 -7 7]+t*[-4 1 -2]=P1+V, where P1 is a point on the line and V is a vector. I then calculated the vector P1P2=P2-P1=[2 7 -7] - [-1 -7 7]=[3 14 -14]. The normal vector of the plane should be parallel to P1P2 im thinking since the plane is perpendicular to the line, but im having a hard time understand and calculating this. I made one attempt where i set n=P1P2XV (cross product) and got the result 1, but the system says it is the wrong answer. Could someone make an attempt to solve this and explain if you got the time?
Result 1: 42*x+50*y+59*z=21
