+3そ20 22 Prove that the line X21+2t ニー+3t is perpendicular to the plane X-2y+zz6

Q: B. Show that line is parallel to plane x-2y + z 6

A:

Q: find the intersection point between the line      X=1+2t {    y=2-t       Z=3 and the x+y-z=3…

A: The intersection point will be common to both the line and the plane. Therefore, substitute the…

Q: Find the intersection between the plane  4x−y+5z=18  and the line through the points  (0,0,1)  and…

A:

Q: Use calculus of variation to derive the shortest line (equation) that joining points (x,y,z) =…

A: Given plane -   7x + 2y + 3z = 7 Parametric equation will be =  (1 - t, 0- 2t, 0 - t) Hence,

Q: Where does the line through (1,0, 1) and (4,– 2,2) intersect the plane x+y+z = 6?

A: It can be assumed that the vector for the coordinate 1,0,1 is 1,0,1 and the vector for the…

Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

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Q: Determine whether the line L : x = 3 – 4t, y= 5+2t, z = 5 + 4t, - is parallel to the plane x - y +…

A:

Q: Prove that the line x +1 = 글(-6) - lies in the plane 3x + y – 2 = 3.

A:

Q: (6) Where does the line through (1,0, 1) and (4, -2, 2) intersect the plane r+y+ z = 6?

A:

Q: 5z' + 3z gral z² - 4 plane, is

A:

Q: sketch the graph xyz plane x^2+z^2=4

A: GIVEN: x2 + z2 = 4

Q: What is the intersection of the plane x+2y+z =0 and the line (x, y,z) = (0,1,2)+ k(–1,1,2), kER?

A: Consider the equation of plane x+2y+z=0 and the equation of line x,y,z=0,1,2+k-1,1,2. Find the…

Q: Find the distance from the point (3, -4, 2) to the a. xy-plane b. yz-plane  c.xz-plane.

A: a) Distance of (3, -4, 2) from xy plane:On xy plane , z=0. So, This point is 2 units away from the…

Q: Show that the plane 2x − y − 3z = 4 is parallel to the line x = −2 + 2t, y = −1 + 4t, z = 4, and…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Where does the line through (1, 0, 1) and (4, −3, 3) intersect the plane x + y + z = 6?   (x, y,…

A: Given points are Given Plane is

Q: Find a plane through the points P1(1, 2, 3), P2(3, 2, 1) and perpendicular to the plane 4x - y + 2z…

A: The given points and the plane are,

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

A: Given lines are x=2t+1, y=-t+2, z=t+1x=2s+2, y=s+3, z=5s+6

Q: Where does the line through (1,0,1) and (4,-2,2) intersect the plane x+y+z=6?

A:

Q: Find the distance between the parallel planes.2x + y - 2z = 0 and 2x + y - 2z = 5

A: The given parallel planes are 2x+y-2z=0  and  2x+y-2z=5. The objective is to find the distance…

Q: Compute x²z ds where Cis the line segment from (0,6,–1) to (4,1,5).

A:

Q: Show that the line x + 1 =y/−1=(z − 2)/2 is in the plane 2x + 4y + z = 0.

A: Given equation of a line, x+1=y-1=z-22 And equation of a plane, 2x+4y+z=0

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

A:

Q: Where does the line through  (−3, 1, 0) and (−1, 7, 8)  intersect the plane  2x + y − z = −2?

A: Given : Points : ( -3 , 1 ,0) and ( -1 ,7,8) Plane : 2x + y - z = -2

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

A: Here, the given equation of the plane is 3x+y-6z=8 So, the coefficients of x,y and z will give us…

Q: int at which the line ⟨4,−1,−5⟩+t⟨−3,3,2⟩⟨4,−1,−5⟩+t⟨−3,3,2⟩ intersects the plane…

A: Given the line 4,-1,-5+t-3,3,2  intersects the plane -x+y+z=18.

Q: Find the point at which the line 7(t) = (5, – 3, - 6) + t( – 2, - 8, 6) intersects the xz plane.

A:

Q: The point (-2,0,8) is. A. In die xy-vlak O In the xy-plane B. In die yz-vlak O In the yz-plane C. In…

A:

Q: Find the distance from the point (2,-3,5) to the plane passes through the points (1,0,-3), (3,4,-6)…

A: (b) Given point P2,−3,5 and a plane passes through the points 1,0,−3, 3,4,−6 We have to find the…

Q: Derermine the pointof intersection of the linel:- [-6,9,-1]+t[-a,3 ,1], t ER, and the plane, TT-x +…

A:

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y - z = -2? (x, y, z)…

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Q: Find the point in which the line through the (3,-1,2) perpendicular to the plane x +2y -5 z = 4…

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Q: The line through the origin whose projection on the xy-plane is a line of slope 3 and whose…

A: In this type of questions we assume a line an points on that line. Suppose we have a line and points…

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

A: Given x=-2, y=4+2t, z=-3+tfor finding intersection with xy-plane , set z-coordinate…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

A:

Q: The line through the point (1, 0, 6) and perpendicular to the plane a + 3y + z = 5

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…

Q: Find √x²ds ds along the line of intersection of the two planes x-y+z=0 and x+y+2z=0, from origin to…

A: The two given planes are x-y+z=0 and x+y+2z=0.

Q: 14) Determine the distance between the parallel planes: 6z = 4y - 2x; and 9z = 1- 3x + 6y.

A: Given problem:- Determine the distance between the parallel planes: 6z = 4y - 2x and 9z = 1 - 3x +…

Q: Find the points at which the line that passes through (–6,6,4) and (12,–6,2) intersects the three…

A:

Q: Find the points of intersection of the line 6. = y+3= z 4 with the plane I+ 3y + 2z – 6 = 0. ОА(-10,…

A: We will solve the following.

Q: Find the point at which the line 7(t) = +t intersects the xy plane. %3D

A:

Q: Find the intersection of the line 1₁: x-6 2 || y+2 1 with the plane p: x-6y - 2z - 10 = 0

A:

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

A: Given : the equation of a plane is  x-y+z=5  and the line passes through (1, -4, 1)  and (4, -10,…

Q: Find the plane determined by the intersecting lines. y = 2+ 4t L1 x= - 1+2t z = 1- 2t L2 x= 1-4s y =…

A:

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y -z = -2?

A:

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.