ü = [1,1, 0] and i = [-1,1,0]. Find the cross product

Q: Find symmetric equations for the line through (1, 3, -2) and perpendicular to both u and v, where u…

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

Q: Find the cross product a × b. a = (7, 0, -3), b= (0, 6, 0) Verify that it is orthogonal to both a…

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

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Q: Find the component of u along v. u - (-2, 4), v- (1//7, 1/v2)

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Q: verify the identity using the formula for the cross product.  (λv) × w = λ(v × w) (λ a scalar)

A: The identity given is  (λv) × w = λ(v × w) (λ a scalar) . To prove the identity ,  let v=i^+j^ and…

Q: Using || || and 0, give the vector in (x, y)-form. II

A: We have to write the x,y form of vector v.

Q: Find the cross product i x v where i = 2i +2j -3k and i = (- 8, – 6, 3). i x ở =

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Q: 1 Y

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Q: Determine ä xb and bxå. Confirm that the cross product is orthogonal to each vector. ā=[4, –3, 5],…

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

A: Solution

Q: Find a nonzero vector parallel to the line of intersection of the two planes 3y+4z=−3 and 5x+y+2z=4

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Q: Find the scalar equation for the plane passing through the point P-(5, 3,-5) and containing the line…

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Q: (3,8, 0) is u x v = %3D So the cross product of u = (1, 0, 1) and v =

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Q: Decompose v into its vertical and horizontal components.

A: Decompose vector v in vertical and horizontal components.

Q: Find the vector equation of the line of intersection of the planes x+y+z=1 and x+2y+2z=1.

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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 a vector function that represents the curve of intersection of two surfaces: z = x² - y? and x²…

A: Idea  1) Solve the equation in term of only one variable (2) assume in term of parametric function…

Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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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: Let = (0,- 2)v=(3,2) and w=(-2,1) Then the dot product u. (V w) is equal to

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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 a vector parallel to the line of intersection of the planes 2x + y - 3z =13 and x + 3y + 5z =-8

A: Given, The equation of the planes  2x+y-3z=13 x+3y+5z=-8 We have to find a vector parallel to the…

Q: Find the cross product a ✕ b. a = (7, 0, −2) , b = (0, 6, 0) Verify that it is orthogonal to both a…

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Q: The scalar component of H parallel to the line y=1, z=2 where H = -2a, + 3as- 4a, at p (1,90, 2) -3…

A: Given: H=-2aρ+3aϕ-4az p=1,90,2

Q: Find the vector equation for the line of intersection of the planes 5x + 2y – 5z = 2 and 5x + 4z = 4…

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Q: Calculate the cross product assuming that u × w = = (4, 8, -3) (-u – 4w) × w =

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Q: Find the cross product a × b. a = (4, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a…

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

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Q: Calculate the cross product assuming that u x v = (4, 3, 0). v x (u + v)

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Q: why you write: s=0, t=0 s=1, t=1  instead of using cross product imediately between 2 vectors…

A: The vectors (1, 0, 1) and (1, -1, 0) are direction or orientation vectors. The cross product of…

Q: Find the scalar equation of the plane that contains the line x+1 -3=. and is parallel to x+2=+4_:+2…

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Q: Prove the property of the cross product u ∙ (v × w) = (u × v) ∙ w

A: Let the vectors , v, and w isu=u1,u2,u3, v=v1,v2,v3 and w=w1,w2,w3

Q: Give an example of a linear combination that resulted in the zero vector that did NOT have 0's for…

A: Query- Give an example of a linear combination that resulted in the zero vector that did NOT have…

Q: Calculate the cross product assuming that u × v =〈1, 1, 0〉, u × w = 〈0, 3, 1〉, v × w = 〈2, −1, 1〉 v…

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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: Q2: Determined the component of the vectors at each point…

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Q: Find a vector that gives the direction of maximum rate of increase for the 6xyz at (-1,2,1) (a)6(2i…

A: To find A vector that gives the direction of maximum rate of increase.

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: Calculate the cross product assuming that u x w иxw3D (2, 6, 1)

A: Given vector u x w <2, 6, 1>

Q: Find the equation of the plane in xyz-space through the point P = (4, 2, 4) and perpendicular to the…

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

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Q: ) Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) =…

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Q: Find an equation of the line that goes through A(0, 1, 4) and is orthogonal to the Y-axis and vector…

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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 vector equation of the line of intersection of the planes x+y+z = 1 and x+2y + 2z = 1.

A: The equation of the line vector of the intersection of 2 planes can be calculated using the cross…

Q: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

Q: Find a vector equation for the line that goes through the points (5,9,0) and (0, 11, 1). F(1) = with…

A: A ( 5,9,0) B ( 0,11,1)

Q: Find the equation of the plane in xyz-space through the point P=(3,3,2) and perpendicular to the…

A: topic - equation of a plane