Calculate the cross product for (i − 3j + 2k) × (j − k)

Q: Convert the integral  0∫2 0∫2z y∫2y dxdydz in the order a) dzdxdy b) dxdzdy

A: Given: ∫02∫02z∫y2ydxdydz

Q: Find a vector parallel to the line of intersection of the planes 2x + 3y – = =11 and 4x + 2y – 3= =…

A: Topic:- vector

Q: Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

A: Given : The equation of the planes are x+ 2y + 6z = 1 and x + 2y + 6z = 10 .

Q: Is {x² – 2.x, x²+x, x²} linearly independent dependent? Prove your answer. or

A: Answer

Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

A:

Q: Q4) Using Green's theorem to evaluate: (12 marks) Sc [ (x3 – xy³)dx + (y³ – 2xy) dy] Where C is the…

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Q: +3そ20 22 Prove that the line X21+2t ニー+3t is perpendicular to the plane X-2y+zz6

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Calculate the cross product assuming that u x w = (-8, -1, -5) (5u + 3w) x w =

A: Solution

Q: Use the given transformation to evaluate the integral. (8x + 8y) da, where R is the parallelogram…

A: Given that vertices of parallelogram is −3,9,3,−9,4,−8  and −2,10 And transformation is x=14u+v  and…

Q: Please solve this problem

A: Given integral is,

Q: Find the trace of the plane 3x − 2y + 5z = 4 in the xy-plane.

A: The given equation of the plane is 3x-2y+5z=4. The trace of the plane in the xy-plane is the…

Q: Let F = cos(5t) i+ 3tj+ 5t° k and G = ° cos(5t) i +²j+5e* k Find the cross product Fx G =

A:

Q: Use the given transformation to evaluate the integral. || 2 Y dA, where R is the parallelogram…

A: Given, ∫∫Rx-4y6x-ydA Where R is the parallelogram enclosed by the lines x-4y=0,x-4y=2 and…

Q: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

A:

Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y-2z=3 is: O0 -3i+6j-3k…

A: Two planes are given: 4x-y+z=2 and 2x+y-2z=3

Q: Bounded by the coordinate planes and the plane 3x + 2y + z = 6

A:

Q: 3] By using the properties of dot and cross product, prove the following: a) (ü x 7). v = 0. b) (w –…

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Q: 2. Use the transformation u = x – 2y, v = 2x + y to find x – 2y 2.x + y Where R is the rectangular…

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Q: (d) Compute the cross product (0, 2, 1) × (1, 3, 1).

A:

Q: Find the distance between these two planes x + 2y –' 2z = 3 and 2x + 4y - 4z = 7.

A: Devide the equation of 2nd plane by 2 .we get that both planes are parallel so just apply formula…

Q: Find the cross product a x b. a = (9, 0, -4), b= (0, 9, 0) Verify that it is orthogonal to both a…

A:

Q: Verify that the operation {x, y} = x1y1 − x1y2 − x2y1 + 3x2y2 where x = (x1, x2) and y = (y1, y2) is…

A: Given : The operation on ℝ2 is defined as  x, y = x1y1 - x1y2 - x2y1 + 3x2y2 ,  where x = (x1 , x2)…

Q: Use the Disk Method Y= x^(3/2) , Y = (3/2)x , revolved around X = 5

A: First we have to design the integral using the given conditions,  and for that obtain functions of…

Q: (1 point) If a = i +j+ 3k and b =i+j+2k Compute the cross product a x b. axb 0 i+0 01

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Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

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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: Calculate the cross product assuming that u x w = (-3, 6, 6) (4u - 4w) × w = |

A:

Q: find the engle of intersection between 2x - 4y + 4z = 7 and 6x + 2y – 3z = 2 .

A: Consider the given planes: 2x-4y+4z=7So,n1→=2,-4,46x+2y-3z=2So,n2→=6,2,-3

Q: What are the perpendicular generators on (D) 좋 =3 %3D2 (P) 16 2. of the surface

A:

Q: Use the transformation u = - -6x +y, to evaluate the integral [ ( (5x • y) dx dy, where R is the…

A: use the transform u=-6x+y, v=5x+ywe evaluate ∫∫R 5x+y dx dywhere R is the parallelogram bounded by…

Q: z= 2e'+i

A:

Q: Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.

A: fx, y=x2y2 Partially differentiating with respect to x, we get ∂f∂x=2xy2 Partially differentiating…

Q: 4. A 5m x 5cm is cut from a corner of 20cm x 30cm. cardboard, find the centroid from the longest…

A:

Q: Calculate the cross product assuming that u x w = (-7, 1, -6) (2u + 4w) x w = = (

A: To calculate the cross product of 2u+4w×w, assuming that u×w=-7, 1, -6.

Q: 24) By using Lagrange multiplier find a point in the plane x+2y+3z=13 nearest to the point (1,1,1)

A: We have to find a point in the plane x+2y+3z=13 nearest to the point 1,1,1 by using Lagrange…

Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: Find the cross product á xb and verify that it is orthogonal to both á and b for á = i+ 33 – 2k and…

A: Given:-a→=i→+3j→-2k→b→=-i→+5k→To find: cross product a→×b→

Q: find the pole and resuidue of 3z + 1 (z + 1)(2z – 1)

A: Poles and residue of the given function are given below ;

Q: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

A:

Q: Find the distance between the two parallel planes 5x – 3y + z – 2 = 0 %3D -10x + 6y – 2z + 3 = 0

A:

Q: Find the distance between the two parallel planes 2x + 4y + 12z=7 and x + 2y + 6z= 10.

A: We have to find

Q: Calculate the cross product assuming that u x w = (-1, -8, -2) %3D (5u + 3w) x w = (

A:

Q: can u help me with pullbacks and integration plz

A: Given that the integral,

Q: Enclosed by the cylinders z= x2 y = x 2 and the planes  z =0 y =4

A: Given: The cylinders z= x2 y = x 2 and the planes  z =0 y =4 The solid enclosed by the surfaces,

Q: Calculate the cross product assuming that u X w = (-2, -3, -2) (2u + 4w) × w = {

A: Given u × w = -2, -3, -2

Q: Find the cemplex fourth routs of Z: 2 J3-22

A: Given, z= 2√3-2i Therefore, r= √[(2√3)²+(2)²] r= √(12+4) r= 4 θ= tan-1(-2/2√3) θ= -30°

Q: Calculate the cross product assuming that u x w = (3, -5, 8) 6. (4u + 2w) x w=

A: We use the properties of cross product (a+b)x w =ax w + b x w Here a=4u and b=2w. Also use the fact…

Q: (x, y) = x¹ 3 1 0 120 001 y, x, y = R³

A: The function <x,y> will be inner product if  1) Non negetivity: <x,x> ≥ 0, for all x and…

Q: Prove the following property of the cross product: u X kv = k(u X v)

A: Let u=u1 i+u2 j+u3 k  &  v=v1 i+v2 j+v3 k. Then, kv=kv1 i+kv2 j+kv3 k Now,…

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

A:

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.