Determine the curvature of 7(t) = (t,t“, t°) V36t4 + 9t² + 4 K А. (9t4 + 4t2 + 1) V36t4 + 36t2 +4 В. K = (9t4 + 4t² + 1)* С. V36t4 + 9t² +1 K : (9t4 + 4t2 + 1) ž D. K = V36t4 + 36t2 +1 (t4 + 4t² + 1)* Е. none of the above

Q: Q10)The two lines L1: x=3-2t, y=4+t ,z= 6-t and L2: x=5-4t, .y=-2+2t, z=7-2t are parallel

A: 10) The equation of the line x=3-2t t=x-3-2 y=4+t t=y-4 z=6-t t=z-6-1

Q: find the angles between the curves v=u2, v=u3, lying on the surface  x=u2+v2 y=u2-v2 z=uv+3u+2v

A: As per the question we are given the parametric form of a surface in 3d as : x = u2 +v2 y = u2 - v2…

Q: ) Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A: Given problem:- Find the vector that parallel to the intersection line of two planes 2x + y - 3z = 2…

Q: Consider the hyperboliode H defined by the equation:  x^2+y^2−z^2=1 and the point P0=(1,4,4) in H.…

A: We are given the following hyperboloid : x2 + y2 - z2 = 1 And we have to choose the correct…

Q: .Calculate the dstance between tve point (3, -2) and the plane Z Xty-2+1=0.

A: The distance between the point (a, b, c) and the plane Ax+By+Cz+D=0 is given by,

Q: Let T be the plane 3x-3y+2z =4. Find the shortest distance d from the point Po-(-5, 1, 4) to T, and…

A: Given 3x-3y+2z=4and P0=-5,1,4

Q: Q3b): Compute zdz over several contours (i) The line from 1 to 1+ i. (ii) The circle of radius 1…

A: let fz=1z.  Since f(z) has an antiderivative in an open region D, then the line integral over given…

Q: Find the coordinates of the midpoint P and Q  P(h, k), Q(h, 0)

A: GivenPh,k,   Q h,0MidpointM=x1+x22 , y1+y22

Q: / Find the distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

A:

Q: y -1 Q2) L, =Xx2 = -1 - 2 Fand equation of plane Canternng them

A:

Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: P5/ Find the Plo,2,-1) and normal to n=3i-2 -k squation tor the plane though

A: Use formula for equation of plane

Q: Find equation of Plane teter mined by the Lines Li. X = t-29 y = 2t+3 Z= +4 and Lz! X…

A:

Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

Q: O O O Find the distance between the two points * (8, 5), (5, 0) 4) V194 В) 12 ) 2v2 D) V34 О в O c D

A: