Consider the curve r(t) that represents the intersection of the surfaces x -4z´ – 2x – 16z –19=0 and y= z+2+ J(z+2)² +1. a. Find the line that passes through (1,2,3) and is parallel to the tangent vector of r(t) at the point 7 ',2, Write you answer in the form L=(x,+at, y, +bt, z, + ct) 4 b. Find the plane that passes through the origin and contains L.

Q: Find the equation of the plane tangent to the following surface at the given points. x +y -z - 57 =…

A: x2+y2-z2-57=7

Q: ind the equation of the plane tagent to the curves f (t) = [3t+4,4 tº, sin (πt) + 4] and g(s) = [8°…

A:

Q: Find the equation for the tangent plane to the surface x-9xyz +y= - 11z at the point (-1,-1,-1). O…

A: The given surface is x2-9xyz+y2=-11z2 and the point is -1,-1,-1.

Q: A line meets a curve y=2x-1 at the point (5,4). The line is tangent to the circde C:x +y² +10x+8y+…

A:

Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

A:

Q: Find the parametric equations of the line perpendicular to l1 and l2 that contains the point (-1.…

A: We have to find equation of a line which is passes through the point (-1,-1,-1) and Perpendicular to…

Q: 2. Find the points of contact of the two tangents to the curve, 6y=2x³+9x³-12x+2, parallel to the…

A:

Q: Find the points on the curve z t? – 10t – 8, y = t² + 4t + 6 that have: A. a horizontal tangent line…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

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.