4 Assuming that the curve ris thex + y +z = 0 intersection of the plane and the sphere , then the curve integralx? + y? + 2? = R? (** + y? +2)ds = ( ). O A 2 В 4 OC TR? D 2xR

Q: Find parametric equations for the line through the point P(3, 6, 4) that is parallel to the plane x…

A:

Q: how was it determined that the equation of the yz plane is x = 0?

A: The objective is to explain yz-plane equals .

Q: Develop vector and parametric equations for the line through (7,2,-1) and parallel to r = (4,7,0) +…

A:

Q: What is the distance from the point P=(2, -1, 4) to the plane 3x+5y-2z =20

A:

Q: Find the distance between two planes if they are parallel x+2y+3z=6 and 2x+4y+6z=5

A: Solution:GIvenx+2y+3z=6  and 2x+4y+6z=5To find the distanceFormula:If θ=0°  then the planes are…

Q: .Calculate the dstance between tve point (3, -2) and the plane Z Xty-2+1=0.

A: The distance between the point (a, b, c) and the plane Ax+By+Cz+D=0 is given by,

Q: Find the equation of the sphere of radius 8 centered at (1, 3, 6). O x² + y² +z² = 46 O x² + y² + z²…

A:

Q: Where does the line with parametric equations −1+3t y = 2 - 2t 2 = 3+ t intersect the plane 3x + y -…

A: Given parametric equation of line x = -1 + 3t y = 2 - 2t z = 3 + t Given plane 3x + y - 4z = -4

Q: Determine an equation for the plane that's tangent to the surface z = 6x2 + 7y2 at point (-3, -2,…

A:

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y? = 8,…

A: Given: The parametric equations for the line tangent to curve of intersection of the surfaces…

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

A:

Q: Q4) Find the intersection of the line x = and the sphere x? + (y – 3)² + (z – 2)² = 4. A) (1,1,0) B)…

A: 1. In analytic geometry, a line and a sphere can intersect in three ways: No intersection at all…

Q: Find a set of parametric equations of a line passing through the point (3,2,-1), parallel to the xz-…

A:

Q: / (2² + y²) do, where S is the portion of the sphere r? + y? + z² = 9 in the first octant that is…

A:

Q: 2. Obtain an equation for a plane 7 that includes straight line(2"--5) and point(-2,1,1).

A:

Q: Li Syaoran is riding an airplane which departs from an airport located at (360, 0) miles in the…

A: The westward speed of the airplane = 480 miles/ hour The northward speed of the airplane = 120…

Q: Suppose C is the line y = 5-2x in the xy-plane. Determine parametric and Cartesian equations of the…

A: Given the line equation C in xy-plane is y=5-2x     put x = k,  in above line . k be a parameter…

Q: P5/ Find the Plo,2,-1) and normal to n=3i-2 -k squation tor the plane though

A: Use formula for equation of plane

Q: b) Find the intersection point of the line Lix-1.y-3+t, z4+2t with xz-plane.

A: Here we have given equation of line and we have to find the point of intersection of given line with…

Q: What is the distance from the point (1,9,3) to the xz-plane?

A:

Q: Let T: R? →R² be a linear transformation that first performs a horizontal shear that into e, - 2e,…

A: The given linear transformation is, T:ℝ2→ℝ2   Since given that T first performs horizontal shear and…

Q: Q2) L, - X+2 +2 ー1 - 2 Frand equaton of plane Coudentg

A: