2. Suppose that S is a surface in R3 with unit normal vector N surface area of S is given by (n1, n2, n3). Show that the do = nįdy A dz + n2dz A dx + nzdx A dy.

Q: construct a normal vector normal to the plane containing the indicated points:   P(-5,0,4)…

A: Three points are given. From these three points we can form two lines  PQ and PR These two lie on…

Q: 32. Find the equation of a plane through the origin and per- pendicular to x – y+ z = 5 and 2x + y–…

A: Note- According to Bartleby guidelines, we are supposed to do only one question. If you want more to…

Q: Let y = Lal: Let L be the line spanned by u. and u %3D Write y as the sum of two orthogonal vectors,…

A:

Q: 3. Let C be the circle x + y = 16 and let S be any surface above the xy-plane with C as its…

A:

Q: 2. Let D be the half-disc in the xy-plane given by x +y <9. 2. Calculate e-?+v}dA Select one: a.…

A: Let  D  be the half-disc  in the xy planegiven  by  x2+y2&lt;9calculate ∫∫D  e-x2+y2  dA

Q: 3. (.J 6) For two vectors u = [1,0,0]" and v = [1,1, 1]", find a third vector with unit length such…

A: Given: Lt us consider the given, u→=1,0,0v→=1,1,1

Q: Let u = (-5,-2, 4), v = (3,6,-5) and w (-7,1,-8). (a) Calculate (u x v). w and hence find the volume…

A:

Q: 8. Find a normal for the plane that passes through the points: P(2,-2, 3), Q (3, 2, 1), R(-1,-4, 2)

A:

Q: a) Let i = xî + yj + zk, r = |7| and å is a constant vector. Find the value of %3D dxr div

A: We will find out the required value.

Q: x-2 z+4 • Let L:*²=+3 = 2²+ and M: 2x - 3y +z = 6 are line and 3 2 5 plane and let P be the…

A: We have to find the equation of line

Q: 12. Find the vector with length 5 and direction angles a = B = 120°, y = 135°. = 60°,

A: 12. Given that a vector with length 5 and direction angles α=60o, β=120o, γ=1350.

Q: The normal line to the surface x² + 2y² + ² = 25 at the point (1, -2, 4) is parallel to the vector O…

A:

Q: 29. Find the volume of the parallelepiped PQRS if the vectors V(PQ). V(PR), and V(PS) are,…

A:

Q: Evaluate F.dr where F(x, v) yi+ejand C is the line segment from (2, 0) to (4,0). a) 0 b) 2 c) - 2 d)…

A: Try to identify line segment then apply on integral part

Q: find the area of triangle between V and W YA (1, 1, 1) V W

A:

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

A:

Q: Assume m₁ = [4., 1.5] and m₂ = [1.5, 0.5] represent the mean vectors of pattern class 1 and class 2,…

A: To find the decision boundary between two classes, we need to find the equation of the line that…

Q: 1. Give the equation of any plane which is has a normal vector n = 2i- j + 3k.

A:

Q: + 2y = xy+1 (n is a constant) nx Answer: Cxy" +xy – 1= 0

A:

Q: 3. Find the to Ihe bae coordinate vector of V relative (l,l, i), ( !!,0), when V= (a,b,c) こ

A: We suppose that (x,y,z) is the coordinate vector of  V relative to given basis so we can write V as…

Q: Two points in rectangular coordinates are given by P₁ (0,0,2) and P₂ (0,1, √3). Obtain the line…

A: We are given points in rectangular coordinates are given by P1(0, 0, 2) and P20, 1, 3. Here, we need…

Q: Calculate the dot product of x = (3, -2, 0, 3) E R and y = (1, 2, 3, 4) ER4.

A: The dot product of two vectors x=(a1,a2,a3,a4)  and  y=(b1,b2,b3,b4)in 4th-dimensional space is: x.y…