If a = i + 3j j k, b = 2i + 4j j 2k and c = = i + 2j + 4k, find a number λ such that d = a + b + λc is parallel to the yz-plane

Q: z dv, where E is enclosed by the paraboloid z = x2 + y² and the plane z = 4. Evaluate

A: see 2nd step

Q: 11. Find the volume of the parallelepiped determined by the vectors u = 2i + 3j - k, i + j - 2k ,…

A:

Q: B) Find the volume of the parallelepiped (box) determined by u, v, and w while: u = 10i + 20j + 50k,…

A: I am going to solve the given problem by using some simple geometry to get the required result.

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

A:

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

A:

Q: 1. Find the volume of the parallelepiped PQRS if the vectors V(PQ), V(PR), and V(PS) are…

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

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 distance from y to the plane in R spanned by the set {u1, uz} 4 - 3 -3 y = -9 -4 Uz 2 4 1…

A: Solution   Given,       Find the distance from  γ to the plane  in R3       spanned  by the  set…

Q: Show that the value of ∮C xy2 dx + (x2y + 2x) dy around any square depends only on the area of the…

A:

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

A:

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: In AQUW, point T is the centroid, and VT = 5 . Find QT and VQ. W V QT= VQ =

A: We know centroid divide each median in 2:1 ratio.

Q: WX || ZY and Zs Z and Y are supplementary WXYZ is a parallelogram Given: Prove: W Y

A: It is given that,  WX ¯|| ZY¯  and ∠Z and ∠Y are supplementary To prove :- WXYZ is a parallelogram

Q: Show that the rank of the linear mapping 7.32. Bar Y3= 301 +302 y = 201 +20203, 31-02-203 1 V2 is…

A: To prove that the rank of the matrix (representing the given linear transformation ) is 2 and to…

Q: Prove that if r(t) has constant length, then r(t) is orthogonal to r'(t).

A:

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

A:

Q: Evaluate // x² zdS, where S is the part of the S 1 + 4x + 3y above the rectangle plane z = [о, 2] x…

A:

Q: Consider the three points in R³ X1 = (-1,5,8), X2 = (1, 3, 7), X3 = (2,6, 4) and let a = x1 – X2, b…

A: Part (a) When two vectors is perpendicular then their dot product is 0.

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

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: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

A: Both vectors v and w lie in the y-z plane, which means they must have zero magnitude component along…

Q: 7. If a =i+ 3j – k, b= 2i+ 4j – 2k and c = -i+2j+ 4k, find a number A such that d= a+b+ Ac is…

A: Given a=i+3j-k b=2i+4j-2k c= -i+2j+4k Find the  λ such that d= a+b+λc is parallel to the yz plane…

Q: B) Find the volume of the parallelepiped (box) determined by u, v, and w while: u = 10i + 20j + 50k,…

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: 1. Find the volume of the parallelepiped PQRS if the vectors V(PQ),v(PR), and v(PS) respectively 31…

A:

Q: H.W 6- Find the volume of the parallelepiped for which the given vectors are three edges. C= 2i +2j…

A: Volume of parallelepiped having a1, a2, a3, b1, b2, b3, c1, c2, c3 vectors as edges is given by…

Q: 10) Find the cross product a x b and verify that it is orthogonal to both a and b. a =  j + 7k,…

A: Let's find.

Q: In APQR, V is the centroid. If QU=54 find QV. S T V R U

A: Centroid is the point of intersection of the medians.we know that centroid divides the each median…

Q: If a = i+3j – k, b = 2i + 4j – 2k and c = -i + 2j +4k, find a number A such that d = a +b+ Xc is…

A:

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

A:

Q: 12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is…

A:

Q: 1 7 Let a, 4 21 and b = 6. 1 2

A: here we can use matrix method to write the equation of plane and then we use the condition that b…

Q: Which of the following planes are not parallel to the plane -x+ 3y + z = 3? Select all that apply. O…

A: Our objective is to find the required plane.

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: In space coordinates, the xy plane consists of all the points of the form O (0, y, z) O (X, y, z) O…

A:

Q: If T is the centroid of MNP, TN=16, MQ=23, and RP=18, find each misiing measure

A: Here T is the centroid of ∆MNPTN = 16,  MQ = 23 and RP =18We find missing measure

Q: Evaluate € fff.₂²². e² dV where E is enclosed by the paraboloid z = 3 + z² + y², the cylinder z² +…

A: We need to find integral.

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 the volume of the parallelepiped shown having    u = 3i − 5j + k ,            v = 2j − 2k and w…

A: Givenu=3i−5j+kv=2j−2kw=3i+j+k

Q: Which of the following planes are not parallel to the plane –x + 3y + z = 3? Select all that apply.…

A:

Q: Find a plane containing t and orthogonal to the pla

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: given vectors u=4i-j and v= 3i+3j compute the projection of v onto u?

A: Given, vector u and v

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

A:

Q: Given v = 6i + 2j and w =i-j, a. Find projwv. b. Decompose v into two vectors v, and V2, where v, is…

A:

Q: Evaluate z dv, where E is enclosed by the paraboloid z = x² + y2 and the plane z = 16.

A:

Q: Evaluate F. dS, where F = 6xy²i + 6x²yj + 2z°k and S is the surface of the unit sphere.

A:

Q: Find a Find a funds on the surdace 7=372y8 at which the feugend Planes is Parallel to the Plane…

A: We have to find the value of points on the surface