a.) Find the vector eq uotion °f the center of the currature of the curve X= y+t. b.) 'det a Lt)= cost e,t te+(2-t-cost) ēg. s how that a is determine the plane and a plane curve, that curve lies in.

Q: A a Search Light has parabolic a youm eflector (has Section that foms. bowl). Jhe parabole bewl wide…

A: Note: There are multiple questions. No specific question has been asked. So, We will solve the first…

Q: Q.7: find the directional parametrization of the line segment joining two point A(2,1,3) and…

A: It is a basic questions of 3-D geometry , we have equate the equation only

Q: 3. Given: F(t) = , a) sketch the plane curve represented by F (indicate the orientation), b) find:…

A: Note: As company policy, we solve first three sub-parts only. Please resubmit the remaining…

Q: EXERCISES 5: Find equations for the (a) tangent plane and (b) normal line at the point Po on the…

A: The plane through a point of a surface that contains the tangent lines to all the curves on the…

Q: 2r2 + y2 7. Consider the equation surface S = P= (1, 1,V3) in the direction of the vector w = (1,…

A: Solution

Q: x + y+ 3z = 0 x-y-z%3D0 2. Find the included angle between the line and the planex -y-z+1 0.

A: we have equation of lines:    x+y+3z=0..... (i)-x+y+z=0..... (ii)Add equation (i) and…

Q: Let u = (5V3, -5). (a) Graph u in the coordinate plane, with initial point (0, 0). y

A: Length and direction of vectors

Q: Sketch the plane curve. (t)-4-. (0,4) y V 10 15 V 10 15

A: Sketch the plane curve

Q: a. Sketch the surface x2 - y2 + z2 = 4. b. Find a vector normal to the surface at (2, -3, 3). Add…

A:

Q: al Let fix,y) = xey². a) Find the equation for the tangent plane to the graph off at (12) b. What…

A:

Q: Q4\A: Find area of zone bounded by curves x = y? 2y = x-3 B: Find area of triangle whose vectors…

A:

Q: O Find equations of the line that passes through the point (2,0,3) and is normal to the plane x – 2y…

A: We will find out the required equation of line.

Q: Find the length of the curve y? = (x – 2)° between the points (2, 0) and (4, 2/2). 22/22 – 2/2 a)-…

A:

Q: a) Mark the points on the contours where Iz = 0. b 2.

A: A contour line or level curve is the intersection of a surface with a horizontal plane. For example…

Q: 8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at…

A: This is problem of vector calculus.

Q: (a) Graph u in the coordinate plane, with initial point (0, 0).   (b) Find the length and direction…

A:

Q: 2. Consider the vector-valued function 12t3 – 72t2 + 96t 15t – 60 6t – 24, if t > 0, t + 4, Ř(t = 4…

A:

Q: Find equations for (a) the tangent plane and (b) the normal line at the point Po(1,2,2) on the…

A: Given, surface is , point is .

Q: Consider the curve F(t) that represents the intersection of the surfaces x + y? -1=0 and y= 2x a.…

A: Given: The curve r(t) represents the intersection of the surfaces x2+y2-1=0 and y=z/2x.

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.