Find the parametric equation for the line where the planes 7x – 6y + z = 10 and 2x + y – 3z = 4 intersect. r(t) + t

Q: 33 and Complete the parametric equations for the line where the planes – 3x – 9y – 12z = - 11x + 2y…

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Q: Complete the parametric equations for the line where the planes - 5x – 2y + 2z = 2 and - 13x + 10y +…

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Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0,1,1).

A: First we find out normal vector to the given plane than find out the point that is closed to the…

Q: Complete the parametric equations for the line where the planes Bz - 4y +22 = 8 and 3z- 14y- 7z = 56…

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Q: Find the distance between the skew lines with parametric equations x 2 + t, y = 1 + 6t, z = 2t, and…

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Q: Find the parametric equation of x, y, z where : . z2 = x2 + y2 p. 9 = x2 + y² Nhat is the name of…

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Q: 17. Find the cartesian equation of the parametric curvex =1+e²*, y= e'. (a) z² = y? – 1 (b) 7 = x² –…

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Q: Complete the parametric equations for the line where the planes -+ 4y+ 13z = - 3x + 5y = 21 and 10…

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Q: 8. The position of a particle moving in the xy-plane is given by the parametric equations x =…

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Q: Find a rectangular equation for the plane curve defined by the parametric equations. x = t + 4, y =…

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Q: Find the angle between the two planes 3x + 2y − z = 7,  x − 4y + 2z = 0 and find a set of parametric…

A: Known fact: The angle between two planes a1x+b1y+c1z+d1=0  and a2x+b2y+c2z+d2=0 is given by…

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

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Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

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Q: Find a parametric equation for the curve of intersection of the cone x²+y² = z² and the plane x+2z =…

A: We have to find a parametric equation for the curve of intersection of the cone x2+y2=z2 and the…

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t,…

A: Explanation: Given that,  Line 1: x=1+ty=1+6tz=2t Vector 1: 1,6,2 Line 2: x=1+2sy=5+15sz=-2+6s…

Q: The line X=t, y+1=t, Z=t intersects the plane. x-2y+Z=2 at the point

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Q: Consider the graph of r(t) = 2t^2i + t^2j + t^3 k Determine parametric equations of the tangent line…

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Q: Find the (perpendicular) distance from the line given by the parametric equations æ(t) 3 – 4t %3D…

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Q: Determine the parametric equations of the curve of intersection of the paraboloid x? – y? + z² = 0…

A: Detailed explanation mentioned below

Q: Find the parametric equations for the line through the point of intersection of the lines L1:x = 2 +…

A: In line L1 and L2  't' is used as parameter but don't confuse with it. Different different line we…

Q: Find parametric equations for the line through P0 = (3, −1, 1) perpendicular to the plane 3x + 5y −…

A: A line L in sace with direction vector d=d1,d2,d3 that asses throughthe point P=(x0,y0,z0) can be…

Q: Find a parametric representation of the solution set of the linear equation.x + y + z = 1

A: Consider the given linear equation  x + y + z = 1 We have one equation and three unknown(x, y, z).…

Q: Find the point at which the line given by the parametric equations below intersects the plane.…

A: Given a system of linear equations are, 2X + 4Y -3Z =-48.................(1) X = 10 +…

Q: Complete the parametric equations for the line where the planes – 8z – 2y – 5z = 0 and - 4x + 2y –…

A: Given: The planes are -8x-2y-5z=0 and -4x+2y-9z=0 To find the parametric equation xt, yt, zt

Q: Find a parametric representation of the line through the point P(3,1,-4) and perpendicular to the…

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Q: Find the distance between the skew lines with parametric equations  x = 1 + t, y = 3 + 6t, z = 2t,…

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Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: x2 +…

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Q: Complete the parametric equations for the line where the planes 8x + 11y + 4z 13x + 2y + 3z = 5…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: Find the general equation of the plane through the point (1, 1, 1) that is perpendicular to the line…

A: We know that equation of plane which passes through pointx1,y1,z1 and perpendicular to linex=x2+at,…

Q: For planes 2x+ y – z = 2 and 2x + 3y + 5z = 4. %3D Write the parametric equations of the line at…

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Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: æ? +…

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Q: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

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Q: Complete the parametric equations for the line where the planes - 7x + y + 3x = 3 and 4x7y + z = 23…

A: Given two planes -7x+y+3z=3 and 4x-7y+z=23

Q: Find the point on the plane x - 2y + 3z = 12 that is closest to the point (0, 2, 2). (x, y, z) =

A: Just I have used the Lagrange multipliers method and find the required solution.…

Q: Find parametrizations for the line in which the planes 3r- 6y – 2z = 3, and 2x+y-2z = 2 intersect.

A: Given Equation of planes 3x-6y-2z=3 and 2x+y-2z=2

Q: Compute the parametric equations of the line in R3 determined by the intersection of the two planes:…

A: To obtain the parametric equations of the intersection line, use the following formulae. Let n1→…

Q: What is the parametric equation for the line through the point (1,2, 3) paralkel to the y- axis? (a)…

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Q: Find the parametric equation for the line where the planes 4x – 6y + 8z = - 36 and – 6y + z = – 15…

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Q: Complete the parametric equations for the line where the planes -4x + 2y – 14z = – 32 and -x – y –…

A: Use parametric equation of tangent line

Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² − z = 0…

A: To find the parametric equations for the intersection of given surfaces.

Q: A cartesian equation of the parametric curve x= 12t + 13 /t – 14, y = vt is OA. X = [ 3y – 2 [ 4y +…

A: We have to find the cartesian equation of the given parametric curve.

Q: Complete the parametric equations for the line wherekche planes 2=0and-2z + 2y + 2z -4 intersect.…

A: The equation of the planes are: P1: 2z = 0 ⇒ z = 0                                  .........1 P2:…

Q: # 2. Let C be the curve that is the intersection of the cylinder x²-2x+4y2 = 0 with the plane z-x…

A: The cylinder x2-2x+4y2=1 and a plane z-x=3. We have to find the parametric equations for the…

Q: B Find the parametric equation of the plane passes through the point (-3,0,7) and perpendicular to…

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Q: Find the (perpendicular) distance from the line given by the parametric equations ¤(t) -2 – 2t y(t)…

A: Solution: The objective is to find the perpendicular distance

Q: Find a parametric function for the intersection of r – 3y + 4z = 0 and a? + y² = 9.

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Q: A curve in the plane is defined parametrically by the equations x = t +t and y t* + 2t2. An equation…

A: The equation of the tangent line is: y-y1=mx-x1 Where m is the slope of the tangent line. And The…

Q: Find the point at which the line with parametric equations x = 3 + 4t, y = 5 – 2t, z = 4 + 7t…

A: According to question,Given equation of line in parametric form,x = 3+4t,y = 5-2t,z= 4 +7t,Equation…

Q: 6. Find the projection of u = -7 onto the -2 line e of R given by the parametric equation l = tũ, -1…

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.