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

Q: B- Find the parametric equations for the line through point (1,0) and parallel to the function f(x,…

A: Given that a line . Find the parametric equation of the given line through point 1,0 and parallel to…

Q: Find a function y = f(x) that describes the parametric x = -2t + 1, y = 3t², for – o <t < ∞. curve

A:

Q: Find the slope of the tangent line to the parametric equations: x = 3t2 - 3, y = 2t + 1 at t = 1. %D…

A:

Q: Find the points on the parametric curve c(t) = (3t2 − 2t, t3 − 6t) where the tangent line has slope…

A: Given curve: So,

Q: find a parametrization for the curve. the left half of the parabola y = x^2 + 2x

A: First, we will find the symmetric line of the given parabola y=x2+2x. We know that the symmetric…

Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y? z1…

A:

Q: Find the parametric equations for the curve of intersection between the cylindrical surface S: x +…

A:

Q: 2. Given the parametric equations: x = t + sin t,y = t- cost, findand

A: Solution...

Q: Find a parametric equation for the line through the point(1,9,3) and perpendicular to the plwne…

A:

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

A:

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

A:

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x - 1)2 + y2/4 = 1…

A: Given: The equation of cylinder is: x-12+y24=1 .....(1) The equation of paraboloid is: x2+y-22=z…

Q: How can I parametrize this 3D shape with two variables? x ≥ 0, 0 ≤ y ≤ x, x^2 + y^2 ≤ z ≤…

A:

Q: Q3/ Find the real number such that the line of parametric equations x = t, y = 2 - t, z= 3+t, is ax…

A:

Q: A curve is defined as the parametric equations: 1 x = acose, y=-asin 0, 0<0< 2n dy where a is a…

A: on solving this we get

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

A:

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

A:

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: Determine the total distance covered from t = 1 to t = 3 from the given parametric equations: x =…

A: Let's find the total distance covered. = d

Q: Determine the area under the parametric curve defined by the equations x-t2-4 and y=t on the…

A: To find: The area under the parametric curve x=t2-4 and y=t on the interval 0,3. Formula used: The…

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² + ¹/² = 4…

A: We need to obtain a set of parametric equations for the curve of intersections of the cylinders:…

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: iminate the parameter in the parametric equations x(f) = 5t – 8 and y(t) = Vt – 5 to find a…

A: Given: The parametric equations are xt=5t-8 and yt=t-5 Given query is to find the Cartesian…

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² +: 4 the…

A: We will use trigonometric identity  sin2t+cos2t=1 and parametric form of standard ellipse to find…

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: What are the parametric equations for the intersection of the planes x - y - z = 1 and 2x + 3y + z…

A:

Q: Find the points on the parametric curve c(t) = (3t 2 − 2t,t 3 − 6t)where the tangent line has slope…

A: This question is taken from the tangent and normal in which we have to find points on the given…

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…

A:

Q: Find the 1st  and 2nd Derivate of y with respect to x from parametric equations.     x=(t-2)5/2…

A:

Q: Find the exact length of the given parametric curve. X = = 8t³, y = 12t², 0 <t< 2

A: Consider the parametric equations

Q: Find the length of the parametric curve: x = 2t + 1; y = t? – 3,0 <t < 5

A: Given that: x=2t+1,  y=t2-3,0≤t≤5To  calculate   dxdt  and   dydt,dxdt=ddt2t+1=2dydt=ddtt2-3=2t

Q: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3]

A: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3].

Q: r(4)=DTsin(i+ 34 j+ t°K 2. POINT: (1,2,1)

A:

Q: Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds…

A: Given: The curve y=4-x2 from (-2,0) to (2,0)

Q: Find a parametric description for the curve x=y^2-9 from (0, 3) to (-5, -2) such that t=0…

A: We need to parametrize the curve x=y2-9 from 0,3 to -5,2 We need to put either x=t or y=t and see a…

Q: Find the length of the curve whose parametric equations are x = 3t^2 and 3t^3, from t = 0 andt = y =…

A:

Q: express the parametric curve in the form y = f (x) c(t) = (4t − 3, 10 − t)

A:

Q: What is the Cartesian form of the parametric equations x(t) = 4t – 2 and y(t) = /t – 3? %3D Provide…

A: To find cartesian form of equation

Q: Find the parametric equation for the line where the planes 7x – 6y + z = 10 and 2x + y – 3z = 4…

A: We have, r(t) = (0, -2, -2) + t(17, 23, 19) The detailed solution is as follows below:

Q: Find the length of the parametric curve x = 2t + 1, y = 3 + 2tž, 0 < t <%.

A: Find the Length of the curve

Q: Find an equation of the tangent plane to the parametric surface x=5rcosθ, y=4rsinθ z=r at the point…

A:

Q: Find the equation of the tangent line(s) to the given set of parametric equations x = t² + 5t – 6 y…

A:

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces tan-1(x?…

A:

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: Find the parametric equations for the curve of intersection between the cylindrical surface S : x +…

A:

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: Eliminate the parameter in the parametric equations x(t) = –7t – 2 and y(t) = Vt – 8 to find a…

A: givenx(t)=-7t-2..................(i)y(t)=t-8..................(ii)we can rewrite 2nd equation…

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: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y² = 8 ,…

A:

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.