Determine the intersection of the three planes below.Group of answer choicesplanelineno intersectionpoint

Let P𝑃 be the plane passing through the points [1,−2,−1][1,−2,−1], [−2,3,−3][−2,3,−3], and [2,0,3][2,0,3].Where does the line [1,3,1]+s[2,−2,0][1,3,1]+𝑠[2,−2,0] intersect this plane?

Which of the following is a plane passing through the points [1,−1,3][1,−1,3], [2,−1,1][2,−1,1], and [0,3,−14][0,3,−14]?Please select all correct answers.[1,−1,3]+s[2,−1,1]+t[−2,4,−15][1,−1,3]+𝑠[2,−1,1]+𝑡[−2,4,−15][1,−1,3]+s[1,0,−2]+t[−1,4,−17][1,−1,3]+𝑠[1,0,−2]+𝑡[−1,4,−17][1,−1,3]+s[1,0,−2]+t[−2,4,−15][1,−1,3]+𝑠[1,0,−2]+𝑡[−2,4,−15][1,−1,3]+s[2,−1,1]+t[0,3,−14]

Consider the planes 3x+5y+2z=1 and 3x+2z=0,（a)find a vector form(with parameter t)for the line of intersectionof the two planes.

Describe the intersection of the three planes u+v+w+z=6 u+w+z=4 and u+w=2(all in four dimentional space). is it a line or a point or a empty set? What is the intersection if the fourth plane u=-1 is included? Find a fourth equation that leaves us with no solution.

Consider the planes 3x+5y+2z=1 and 3x+2z=0,(a)find the unique point P on the y-axis which is on both planes.(b)find a unit vector v with positive first coordinate that is a parallel to both planes.(c)use parts(a) and (b) to find a vector form(with parameter t)for the line of intersectionof the two planes.