O Find the distonce from the point pC1,\, 1) to the plane 2K-3y+72=1

Q: Q1 Consider the planes. 7: 2x-y+z = 6, : x+y+22=3,, 3x-4 y+sz=10 : 2x-y +2=3,52-3y+22=1, Find the…

A: Consider the planes: π1: 2x-y+z=6, π2: x+y+2z=3, π3: 3x-4y+5z=10 and  π4: 2x-y+z=3 .   Find angles…

Q: Find parametrizations for the lines in which the planes x + y + z = 1, x + y = 2

A:

Q: Show by Vector mothads that th ditonce hom fhe fornt P.(Xx, Y,, Z) to the plane Ax -+By+cz-D26 t of…

A:

Q: Find a vected that is Perpenditular to the Plane that Contaiins the e poin +s P(2,3,4), Q~2)0,5), R…

A: Given: The three points:  P (1 , 3 , 4 ) , Q ( - 1 , 0 , 5 ) and R ( 4 , 2 , 2 ).   To determine: A…

Q: (b) Let the distance between two adjacent planes parallel to the plane (hkf) in the direct lattice…

A:

Q: Compute the distance d from y to the plane in R' spanned by u1 and uz.

A: We have to find the distance d from y to the plane in R^3.

Q: Show that the area of that portion of the surface of the paraboloid x² + y² = 4z included between…

A: Here we need to find area between given plane and x*x + y*y = 4z

Q: Evaluate / x2 zdS, where S is the part of the plane z = 4+ 3x + y above the rectangle [0, 4] x [0,…

A:

Q: a) Show that the distance between the parallel planes Ax + By + Cz = D1 and Ax + By + Cz = D2 is |D1…

A: (a) To show that the distance between two parallel planes Ax+By+Cz=D1 and Ax+By+Cz=D2 is…

Q: a) Evaluate (-ri-yj+2z k) n dS, where a is the portion of the paraboloid : 3x +3y between the planes…

A: We have to Evaluate the Integral using polar coordinate

Q: Find the eguatien of the tangett line and nemat plane to the cune; Y. cest Ces(zt)i + st sinCet) j +…

A: Given r=cost cos2ti+cost sin2tj+sintk

Q: Q) show that the pánts ACI,1,4), B(2,2,2), C (o,1,5) and D(1,0,5) ave coplanear (in the Same plane).

A: The given points are: A=1,1,4B=2,2,2C=0,1,5D=1,0,5 To prove: A, B, C and D are coplanar (they lie in…

Q: Calculate f((5x + 2y)i + (4x + 7y) 3) · dr where C' is the circular path with center (a, b) and…

A:

Q: What is the projection of r(t) = ti + t4j + etk onto the xz-plane?

A: Given: r(t)= ti+t4j+etk

Q: I, Use Stoke's theorem to evalueate S.Fidr, where F Cau2)= - it +x3 + 2î aind C is the Ceurve of…

A:

Q: Find a formula for the distance from the point P(x, y, z) to the (a) xy-plane (b) yz-plane (c)…

A: Distance between two points x1, y1, z1 and x2, y2, z2 is given by x2-x12+y2-y12+z2-z12.

Q: Which of the following planes is parallel to the plane 3x – 2y + z= 3? - Oz=3x- 2y + 9 z = 6x- 4y +…

A:

Q: Evaluate x* zdS, where S is the part of the plane z = 1+4x + 3y above the rectangle [0, 3] x [0, 5]

A: Please see the below picture for detailed solution.

Q: Find all planes in R3 whose intersection with the xy-plane is the liner( t) = t ( 2, 1, 0) .

A: GIVEN  Intersection with the xy-plane is the line r( t) = t ( 2, 1, 0)

Q: Show there is no plane perpendicular to n=i+jn=i+j that passes through points P(1,2,3)P(1,2,3) and…

A: This is the rough image Point P(1,2,3) and Q(2,3,4) are the points on the plane…

Q: Find the area of the part of the paraboloid z=x² + y² that lies under the plane z=9.

A:

Q: Show thata perojective plane of gives 0nder indeed BİBD (+n+l, n+),1)

A: We need to show that the projective plane of order n indeed gives a BIBD (n2+n+1,n+1,1)

Q: Find the projection in the ry plane of the curve of intersection of the surfaces 222 = r² + y? and r…

A: Find your answer below

Q: Calculate Se(5x + 3y) i + (4x + 3y) j) · dĩ where C is the circular path with center (a, b) and…

A:

Q: Find the surface area of the part of the plane z = 4+ 7x + 6y that lies above the rectangle [1, 6] ×…

A: We can use integral calculus to find the surface area of the part of the plane above the given…

Q: Evaluate Sf,(z+ 3y – x²) dS where S is the portion of z = 2 – 3y + x² that lies over the triangle in…

A: Ans :

Q: a) Evaluate [-ri-yj+2: k) - n ds, (-a i- where a is the portion of the paraboloid z = 3r + 3y…

A:

Q: Prove that the distance d from a point P (xo, Yo, 2o) to the plane r: Ar + By + Cz + D = 0 is given…

A:

Q: Show that the minimum distance from the origin to a point on the plane ax + by + cz = d is |d| Ja? +…

A: Given :               ax + by + cz = d         We know that minimum distance (p) of a point x1,y1,z1…

Q: Find a formula for the distance from the point P(x, y, z) to the a. xy-plane . b. yz-plane c.…

A: a) xy plane is given by z=0 We have to find distance of (x,y,z) from z=0

Q: Use the Green's theorem to calulate So (3x²y – xy? – 3.x²y²) dx + (x³ – 2.x³y+ x²y) dy, where C is…

A:

Q: Use Stoke 's Theorem to evaluate [ V. dr, where v= y²i + xyj + xzk, and c is the bounding curve of…

A:

Q: O Find an equahion for the plane throught (1,-,3) parallel to the plane 3xy+Z=7

A: According to q&a guidelines I can do only 1question

Q: Evaluate x2 zdS, where S is the part of the S plane z = 1+ 2x + 3y above the rectangle [0, 2] × [0,…

A: We have to evaluate ∬Sx2zdS, where S is the part of the plane z=1+2x+3y above the rectangle 0,2×0,3.…

Q: R) show that the pints ACI,l,4), B(2,2,2), c (o,1,5) and D(1,0,5) are coplanear (in the Same plane).

A: Form the three vectors and take the determinant of them. If determinant equal to zero it means all…

Q: Calculate ff A.n ds If A = yi + 2xj – zk and S is a 2x + y = 6 plane surface in the first octane cut…

A:

Q: Find the projection in the ry plane of the curve of intersection of the surfaces 2z2 = r? + y? and…

A: Let's find.

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

A: Surface integral

Q: Find a parametrization for the line segment beginning at P, and ending at P2. P (2,-3,2) and P2(0, –…

A:

Q: a) Evaluate /| (-ri-yj+2: k) · n dS, where o is the portion of the paraboloid z = 3x2 + 3y? between…

A: Define a function fx,y=z or fx,y=3x2+3y2.  So, the flux integral is:…

Q: tor that is norma to the Plane determined by the three Points i+ 2j +k, si-j+ k , 3i + 2; - 7k.

A:

Q: Find the envelope of the plane 1, C + u + a + и b + u mere u is the parameter.

A:

Q: Let D* be a parallelogram in the uv-plane with vertices A*(o)0), B*(를/듣), C*(를 ') E*( ).Let D be a…

A:

Q: Show that a indeed perojective plane of gives 0rder BİBD (n+n+,n+),!

A: We need to prove that a projective plane of order n indeed gives a BIBD (n2+n+1, n+1, 1)

Q: The distance from a point S(xo, Yo, Zo) to a plane M: ax + by + cz + d = 0 is given by In PS| d :…

A:

Q: Evaluate JJ (² where o is the first-octant portion of the plane 2x + y + 2z = 6 (x² + 2yz)dS

A:

Q: Let P be the plane with equation −x+2y−2z = 3. Find four distinct points on P at distance 3√10 to…

A:

Q: Evaluate Sſ Ands where A= (x+y*)î – 4xj +4yzk and s is the surface of the plane, 2x+y+2z=8 in the…

A:

Q: Find the area of the part of the plane  5x + 3y + z = 15  that lies in the first octant.

A: From the given statement, the plane is 5x + 3y + z = 15 and it is lies in the first octant.

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.