Find the planes tangent to the following surfaces at the indicated points. (a) x² + 2y² + 9xz = 12, at the point (1, 2, 3 (b) y² -x² - = 8, at the point (1, 3, 7) (c) xyz = 1, at the point (1, 1, 1)

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: 2 2. Find an equation of the plane containing the point P(0, -) and the line determined by the two…

A:

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Find the coordinates of the point p on the plane #₁ - 2 + 2x3 = 0, that is closest to the point b =…

A: x1-x2+2x3=0  that is closest to the point (2,0,-2)

Q: Find the point on the plane x+y+z=-46 that is closest to the point (1,1,1).

A:

Q: Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

A:

Q: 3. Find an equation of the plane parallel to the plane 4x -z- 3y -4 = 0 and passes through the point…

A:

Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

A:

Q: Determine the point at which the line passing through the points P(1, 0, 6) and Q(7, -1, 7)…

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…