Let L. be the line passing through the point P=(5, 1, 1) with direction vector [-1,5, -2], and let T be the plane defined by 2xry-32--9. Find the point Q where Land T intersect Q=(0.0.0)

Q: be the line through the point with coordinates (0,1,0) in the direction of the vector h of the…

A:

Q: Let L₁ be the line passing through the points Q₁-(-1.-3, 1) and Q₂-(-4,-6, 2). Find a value of k so…

A:

Q: Find an equation of a plane containing the line r (-3, -3, -5)+t(4, 4, -2) which is parallel to the…

A: A plane containing the line r=-3, -3, -5+t4, 4, -2 which is parallel to the plane -2x+y-2z=8. We…

Q: Let L, be the line passing through the point P=(8, -6, 0) with direction vector a=-3, 3, 1]", and…

A: Given, L1 is the line passing through the point P1=8,-6,0 with the direction vector d1→=-3,3,1T. So,…

Q: Find an equation of the plane through (-7, 2, 1) that is 2 = 3t, y +3 = 6t, z = perpendicular to the…

A: We know that equation of plane passing through the point (x1,y1,z1) and normal n=ai+bj+ck is…

Q: Let A be the point with coordinates (1, 9, 5), let B be the point with coordinates (-3, 5, 1), let C…

A: Given coordinates are, A=1,9,5B=-3,5,1 So, the midpoints of AB is C1-32,9+52,5+12=C-1,7,3.

Q: Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector…

A:

Q: nterseeting Lines Finad the plane determined by the Loi Xi=l-2t, , J="l-st,, 2= -2+t, L2: X2=-3+t2,…

A:

Q: Let Lz be the line passing through the point P-(10, 1. –10) with direction vector d--2, -2, 3]", and…

A: We will use formula for the shortest distance.

Q: Let L. be the line passing through the point P-(4, -3, 1) with direction vector a-[-4, 1, 1], and…

A:

Q: Q3// :- Write an equation for the plane containing points P=(1,1,-2),Q=(0,2,1), and R=(-1,-1,0)

A:

Q: Let Lz be the line passing through the points Q1=(1, 3, 1) and Q2=(7, 12, 4). Find a value of k so…

A: We will solve the problem

Q: Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A:

Q: Let /be the line through the point with coordinates (2,-1,0) in the direction of the vector G) 1…

A:

Q: Let L, be the line passing through the point P-(1, -7, 5) with direction vector d-[1,-2, 0], and let…

A:

Q: Find the distance between (1,-2, - 1)and the plane through the points (1, 2, 3)and (3 , 2, 1)and…

A: Given information: The plane passes through the points (1, 2, 3) and (3 , 2, 1) and perpendicular to…