Question

Please complete number 30 and explain step by step, thankyou.

In Exercise 30-33, find the intersection of the line and plane. x+y+z=14 r(t)=(1,1,0)+t(0,2,4) 2x+y=3, r(t)=(2,-1,-1)+t(1,2,-4) z=12, r(t)=t(-6,9,36) x-z=6, r(t)=(1,0,-1)+t(4,9,2) Verify that the plane x-y+5z=10 and the line r(t)=(1,0,1)+t(-2,1,1) intersect at P=(-3,2,3). The plane 3x-4y+2z=8 intersects the xy-plane in a line. What is the equation of this line? In Exercise 36-41, find the trace of the plane in the given coordinate plane.

Show transcribed image text In Exercise 30-33, find the intersection of the line and plane. x+y+z=14 r(t)=(1,1,0)+t(0,2,4) 2x+y=3, r(t)=(2,-1,-1)+t(1,2,-4) z=12, r(t)=t(-6,9,36) x-z=6, r(t)=(1,0,-1)+t(4,9,2) Verify that the plane x-y+5z=10 and the line r(t)=(1,0,1)+t(-2,1,1) intersect at P=(-3,2,3). The plane 3x-4y+2z=8 intersects the xy-plane in a line. What is the equation of this line? In Exercise 36-41, find the trace of the plane in the given coordinate plane.