. [V] Find a parametrization of the plane that contains both the point (2, 4, 6) and the line x = 7 − 3t, y = 3 + 4t, z = 5 + 2t.

Q: Q2: Find the point of intersection of the lines x = 2t + 1, y = 3t + 2, z = 4t + 3, and x = s + 2, y…

A: Solution

Q: 6. [8.5] Consider the points A(1, 3, 1), B (2, 1, 0), and C(5, 1, 1). Determine the Cartesian…

A:

Q: 7. a) Find the equation of the plane passes through the point P(1,2,-1), perpendicular to…

A: We have to solve given problems:

Q: Find a plane through P (2, 1, 1) and perpendicular to the line of intersec- tion of the planes:…

A: find a plane through P2,1,1 and perpendicular to the line of intersection of the planes  2x+y-z=3 ,…

Q: Find the value of k so that the line [x, y, z] = [2, -2, 0] + t[3, 5, k] is parallel to the plane 4x…

A:

Q: Let 5x + 3y + 10% = 0 be the equation of the 3 plane in R³ spanned by (1, a, 0) and (1,0, b). Find…

A:

Q: [V] Find the three intercepts of the plane 3x +y + 2z = 12 and use them to sketch the plane. How…

A: Here we have to find the three intercepts of the plane 3x +y + 2z = 12 and use them to sketch the…

Q: Q3: Find the distance between the origin and the plane containing the points A(1,1,0), B(-1,0,1) and…

A:

Q: Find the distance between the line 2x - 3y + z = 6, 2y- z = 4, and the plane passing through the…

A:

Q: Find the distance from the point (1,1,1) to the plane 2x+2y+z=0

A: Solution :-

Q: 285. Find the scalar equation of the plane that passes through point P(-1, 2, 1) and is…

A:

Q: Find an equation of the plane that passes through the line of intersection of the planes ( x – z = 1…

A: We have found the plane that passes through the line of intersection of the planes x-z=1 &…

Q: Find the point of intersection of the line with equation L: (x,y,z) = (1, - 1,0) + t(1,1,2) and the…

A: To find the intersecting point, we substitute the values of x, y, and z in the equation of plane and…

Q: Q2:Prove that the line (x-1)/2=(y+1)/3=(z-2)/(4 ) is parallel to the plane x-2y+z=6 ?

A: