Find the cross product á xb and verify that it is orthogonal to both á and b for á = i+ 33 – 2k and b = -i+ 5k.

Q: Find the cross product u x v where i = 3i +6j +9k and v = (- 2, – 4, 5). ux v =

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Q: The dot product of two vectors Y1 Y2 and j = Yn in R" is defined by a · j = x11 + x2y2 + ...+ x„Yn-…

A: According to the given information, it is required to determine a vector in R3 that is perpendicular…

Q: (a) a = (2, 6, 0) , b = (4, –1, 1) (b) a =i-j-k, b = }i+j- 4k

A: a) given that  a=<2,6,0> , b=<4,-1,1> a→=2i+6j+0kb→=4i-j+ka→×b→=ijk2604-11…

Q: The unit vector which is perpendicular to both r138ax+3ay-2az, * r2=2ax+7ay-6az is equal to a)…

A: As per our guidelines, we are allowed to answer only question. Since, you have posted multiple…

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

A: Given, i-3j+2k×j-k To solve the above cross product.

Q: Find the cross product u x 7 where u = 51 -3j+k and = (-1, -3,2). uxv=

A: To find the cross product u→×v→ where u→=5i-3j+k and v→=-1, -3, 2.

Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

Q: Find the trace of the plane 8x – 9y + 2z = -11 in the coordinate xz-plane.

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Q: find the trace of the plane in the given coordinate plane.  −x + y = 4, xz

A: Find trace of the plane in the coordinate plane -x+y=4 in xz

Q: Use the transformation u = y – 3x, v = y + 6x to evaluate // (2y + 12x) dA on the parallelogram R…

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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: Find the cross product a x b. a =j+ 9k, b = 4i - j + 2k Verify that it is orthogonal to both a and…

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Q: Also deduce the Jacobi identity for the cross product: u × (v × w) +w × (u × v) +v × (w x u) = 0 их

A: Introduction: We know that u×v×w=vu·w-wu·v, where u, v, and w are purely imaginary.

Q: Find the next vector spacing and wrap A = 1(x + y?) +jv² + zx) + k(z? + xy)

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

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Q: Find the cross product a x b. a ++kb-i+2j - 3k 10 Verify that it is orthogonal to both a and b. (a x…

A: Consider the vectors  a=12i+13j+110k,    b=i+2j-3k

Q: Find u × v and show that it is orthogonal to both u and v.u = j + 6k, v = 2i − k

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Q: 45. Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

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Q: please help me with this exercise

A: Given,

Q: please help me with this exercise

A: The given vectors are

Q: Find the cross product ⃗a × b and then specifically verify that it is orthogonal to both ⃗a and b:…

A: Given data:     The first vector is: a=<a1, a2, a3>=<6, 0,-2> The second vector is:…

Q: Find the cross product a x b. a = i-j- k, b = i + j+k Verify that it is orthogonal to both a and b.…

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

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Q: Given v = - 3i + 5j and w = i+j, a. Find projwv. b. Decompose v into two vectors V1 and V2, where V1…

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Q: Find the component of u = 2i + j − 3k that orthogonal to v = 3i – j, then verify your result.

A: This question can be solved using the concept of component of vectors.

Q: Find the cross product a × b. a = (2, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a…

A: We can find each of them by using the besic definition

Q: Find the cross product a X b. a = (4, 5, 0), b = (1, 0, 9) Verify that it is orthogonal to both a…

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Q: Find the cross product axb. 1+9k, b- 41-j+ 3k Verify that it is orthogonal to both a and b (a xb) (a…

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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: 8) Find the cross product a x b and verify that it is orthogonal to both a and b. a = (1, 1, -1),…

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Q: Calculate the cross product assuming that u X w = (7, 6, 2) (-3u + 4w) × w =

A: We need to find cross product.

Q: Find the vector, not with determinants, but by using properties of cross products. k x (i - 2j)

A: The product of the vector helps to find the required product. The answer to the product is whereas…

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: Find the cross product a × b. a-i-j-k, b-tj+* Verify that it is orthogonal to both a and b. (a x b)…

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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 coordinates of the reflection without using the coordinate plane. P (4,6) over the x-axis.

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Q: Calculate the cross product. (i - 9j + 6k) x (j – k)

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Q: Determine the value of kk so that these planes in R^3: 3kx+y−5kz=-10 2x−3y+z=−12 are orthogonal.…

A: Given: The planes 3kx+y−5kz=-10 and 2x−3y+z=−12 are orthogonal.

Q: Find the condition for the points(a, 0).(h, k)(0, b) when ab 0 to be collinear.

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

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Q: Find the distance between the following parallel planes: (a) 3x – 4y +z=1 and 6x – 8y + 2z =3 (b) –…

A: Solve the above questions.

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

A: Given u × w = -2, -3, -2

Q: please help me with this exercise

A: To find the cross product, we form a determinant the first row of which is a unit vector, the second…

Q: 3. Find the cross product u X v when u = and v = .

A: Here we have to find the cross product of two vector.

Q: Find the cross product a x b. a = j + 6k, b = 31 - j + 2k Verify that it is orthogonal to both a and…

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Q: Find the cross product a x b. a = (t, 2, 1/t). b = (r?, r², 1) Verify that it is orthogonal to both…

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Q: -:Q1 Evaluate , (x- 2y) dA, where R is the parallelogram in the xy-plane with vertices (0,0), (4,1),…

A: The objective is to evaluate ∫∫Rx-2ydA where R is the parallelogram in the xy plane with vertices…

Q: Find the cross product a x b. a = (1, 1, -1), b= (2, 8, 10) Verify that it is orthogonal to both a…

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Q: Find the cross product a x b. a = i + 4j – 2k, b = -i + 4k Verify that it is orthogonal to both a…

A: The cross product of a and b is:

Q: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…