The shape of the coordinate curves of cylindrical (p, Ø, z) coordinate systems are O straight lines, circles, and straight lines respectively o straight lines, circles, and semi-circles respectively. O straight lines, semi-circles, and circles respectively. O None of these

Q: P Flag question Find Vx F at the point (-1, 1, 2) if F(z, y, z) = (3x°y² – 3zy²)i + (2yz³ – 18yz)j+…

A: We have to curl of function at the given point

Q: 3.2 a. For what values of c is the set of equation Y₁ = x²+y³ +z = c a smooth surface? b. Sketch…

A: For (a), We need to find the values of c for the set of equation Yc=x2+y3+z4=c to be a smooth…

Q: The equations of the lines 1 and l, are r = 2| 2 | and r = µ 3 respectively, where 1, µER. -2 The…

A: Using vector equation of angle bisectors, line passing through origin,

Q: The direction angles of a nonzero vector a are the angles a, ß, and y (in the interval [0, m]) that…

A: We need to find direction cosine and angles.

Q: Vector a is given such that a = (2, – 3, 1) Which of these vectors b = (2, 2, 2) c= (4, – 1, 0) d =…

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Q: The intersection of the two planes given by the vector equations -2 (2). -3 and is -4 4 -6 = -3 = 4…

A: We have to find equation of intersection of two planes.

Q: Vectors Question 5 Fill in the correct numbers or choose the correct answer. Let u=(1,0,1),…

A: We will find out the required value.

Q: A line in space is described algebraically by using equations. The line that passes through the…

A: A line in space is described algebraically by using _________ equations. The line that passes…

Q: QUESTION 5 If 3 vectors V1, V2, V3 in R' span all of R3, then { True O False QUESTION 6 If 3 vectors…

A:

Q: v  =  { 1 , 2 , −1 }  ;  w  =  { 2 , −4 , 0 }    the angle between the two vectors…

A:

Q: Let u= = (2, 4, 2), v = (0, -1,2), and w = (-5,2,1). (a) Plot u, v, and won the same set of axes.…

A: If a→=a1, a2, a3 and b→=b1, b2, b3, then a→·b→=a1b1+a2b2+a3b3. It can also be written that:…

Q: 37. The plane that passes through the point (3, 1, 4) and contains the line of intersection of the…

A: 37. The given data is: The equation of planes are: x+2y+3z=1            .......12x-y+z=-3…

Q: Section 2.1 17) Given: m lln Transversal K m23 =4xty €, 68 Mce =4x+74 %3D Find:x,yand m<7

A: Lines and Angles

Q: Find the requested equations below Find some symmetric equations for the line with point P(4, -4,…

A:

Q: 6 What vector v is given by the coordinate vector 3 ? 6 B = { [−3 8 7], [7 1 6], [7 −4 9]}. B

A:

Q: In the adjoining figure, point Q is the center of the top face, and R is midpoint of the segment. |2…

A:

Q: The line / passes through the points with position vectors 2i – 3j + 5k and 7j + k. Given the point…

A: Given points are (2,-3,5) and (0,7,1)  So the direction ratio of the line= (2,-3,5) - (0,7,1)=…

Q: Find an equation of the plane that passes through the points M(1,2,3), N(-3,-2,5), and 0(2,-3,4).

A: I am going to solve the given problem by using some simple geometry to get the required result.

Q: Betermine the value of k for which the following planes are perpendicular: π₁ = (1, 2,7) + s(4,2,0)…

A: π1 = (1,2,7)+s(4,2,0)+t(k,1,2)  First need to find the normal of the planeIf the plane in the form…

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.