4. Suppose that VxF= (0,1,-1), S is the plane x + y + z = 1 in the first octant and Cis the boundary of S. Then OF dr equals C (a) 0. (b) a. (c) 3.

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Given, through the point (4, 2, -5) and perpendicular to the plane…

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

A:

Q: 10. Find the equation of the plane containing the line x = 1+t, y=-1-t, z = −3+2t and that is…

A:

Q: The integer n = 12700140x3243243 is missing the digit x. a) If n congruent to  3 (mod 9), then what…

A: According to the given information, Consider the given integer n:

Q: Find the equation of the plane that contains the line x = 1+t, y = 2+2t, z = 3- (1, -2,4). e point p…

A:

Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

A:

Q: Given are the following two lines: ₁ (s) = -2 + 3 1 2 0 S and ₂ (t) = 3 () - ()₁ 1 t 3 a) Show that…

A:

Q: x-2 z+4 • Let L:*²=+3 = 2²+ and M: 2x - 3y +z = 6 are line and 3 2 5 plane and let P be the…

A: We have to find the equation of line

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: 12. Find the vector with length 5 and direction angles a = B = 120°, y = 135°. = 60°,

A: 12. Given that a vector with length 5 and direction angles α=60o, β=120o, γ=1350.

Q: 5. Among all the points on the graph of z = 10 – x² – y² that lie above the plane r+2y +3z = 0, find…

A:

Q: 10. Find an equation of the plane that passes through the points (x, y, z) = (1, 2, −1), (x, y, z) =…

A:

Q: 4. Calculate the perpendicular distance between the plane with axis intercepts P(4, 0, 0), Q(0, 3,…

A: Answer is: 0.53846153846153846 Solution is given below:

Q: x =1+t Is the point (1, 2, 5) closer to the line L'(t)- y = 2+t z = 3+t or the plane 2x +3y+6z=12?

A: The distance between a line and a point can be calculated by the formula d=MoM1×s→s. Here, M0 is the…

Q: Let p be the line given (a) Compute the distance between p and the line (b) Compute the distance…

A: The given line and plane are:p: x+25=-y2=z-25∑:3x+5y-z=4 We know that distance between two lines…

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: (a) Find two points on the line x = -1+3t, y=t + 2, z= 2t – 7. (b) ( Find The point at which the…

A: Equation are given in parametric form: Vary parametric value for different points.

Q: 19. If F(2, y, z) = (2xz, 3y - 22,1 + a2) and C is the path along a2 + y? 1 in the plane z = 0 from…

A: To find: Work done by the field on the particle moving along the loop.

Q: 2. Consider the line r(t) = (4t+1,3, 2 - t) and the ellipsoid + + z? = 1. What is the distance from…

A: Consider the line  and the ellipsoid To find  distance from the point (-3,3,3) on the line to the…

Q: with the guldin's proposition 1 get the contents of the rotating object that occurs if the land…

A: As per the question we are given a 2d region bounded by the curve : y = 6 - 3x - x2 and the straight…

Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.