By analysing the normals, determine if the three planes intersect in a point. T₁: X-5y + 2z-10 = 0 ₂: [x, y, z]= [0, 0, 3] + s[2, 0, 1] + t[7, -1, 0] 2 13: 8x + 5y +z - 20 = 0

Q: Find the equation for the tangent plane and the normal line at the point Po(1,2,1) on the surface…

A: The given problem is to find the equation of tangent plane to the surface and equation of normal…

Q: Find the orthogonal trajectories of the family of lines 3x + 5y = C A B C D 3x 5y = k 5x 3y = k 3x +…

A: Orthogonal trajectory

Q: Let C = (-2, -1) be the center of dilation. Let X = (1, 1), Y = (3, 0) and Z = (2,5). Our dilation…

A: Center of dilation=-2, -1X=1, 1, Y=3, 0, Z=2, 5Dilation factor, k=3

Q: 8. Find a normal for the plane that passes through the points: P(2,-2, 3), Q (3, 2, 1), R(-1,-4, 2)

A:

Q: Which of the following is the normal plane equation to the curve that is the intersection of both…

A: To determine the normal plane equation to the curve at the intersection of the two given surfaces at…

Q: Find equations for the lines tangent and normal to the cissoid of Diocles y² (8-x) = 16x³ at (4,16).…

A:

Q: Find the point at which the line r(t) = (7, −7, 4) + t(−6, 6, −8) intersects the az plane.…

A: To find the point where the line intersects xz plane

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: x = 1+2t Determine the distance between the lines L₁ y=-1-t, tЄR • z = 3t and L2: T = (1, 2, 3 1, 2,…

A: Step 1: Step 2: Step 3: Step 4:

Q: X= 5 +t The parametric equations of a plane are y = 1+t. Find a scalar equation of the plane. |z=1-s…

A: As per the company's guidelines, we are supposed to answer the first question for you, Kindly repost…

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

A:

Q: ind the point of intersection for the lines v(t) = (-5, - 8, -6)t + (− 1, 3, 1) and (u) = (6, 6, 2)u…

A: First we find value of parameters u and t .

Q: Select all lines that are parallel to the plane x+y+z%= 3. OF(t) = (1,1, 1) + t(1, 1, –2) OF(t) =…

A:

Q: Use an appropriate change of variables to compute Se (x – y)e(x²-y²)dA where R is the rectangle…

A: Use change of variables: u=x-y and v=x+y or x=v+u2 and y=v-u2.  Calculate jacobian:…