2 Let I be the line in R³ that consists of all scalar multiples of the vector w = -[] 2 Find the reflection of the vector v = reflection = [8] 8 in the line L.

Q: 2. Find an equation (parametric and vector form) of the line if the line is perpendicular to the…

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Q: Let L. be the line passing through the point P=(5, 1, 1) with direction vector [-1,5, -2], and let T…

A: Solution :

Q: 5. Suppose z = f (x, y), where x= g(s,t)and y= h(s,t). Show that ôz d²x ¸ ôz ô²y %3D ô°z ôx ôy ôz(…

A: Chain rule of partial derivatives: Let us consider a two variable function  z=f(x,y)  where ,…

Q: Compute the orthogonal projection of v = proj, (v) = -5 onto the line L through -4 and the origin. 6…

A: Introduction:  The vector projection of a vector a on (or onto) a nonzero vector b, sometimes…

Q: Find a scalar equation of the plane containing the line and the point (-5, -1,5). x = 6 +8t, y=-1-3t…

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Q: Given a point M = (5,–3,–2) on a line in space and a parallel vector to the line defined as vector d…

A: Parametric equations of a line  in 3-D space are given byx = x0 + t a , y = y0 + t b , z = z0 + t c…

Q: Find a vector orthogonal to the line x+y=1

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

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Q: 7. Find the scalar equation of any plane which contains the line = (1,2,1)+ t(3,6,-1)

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Q: Find the scalar equation for each line: (a) a line through the point (-6, 7) with direction vector…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

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Q: The velocity vector of a particle in the xy-plane is (√7, 9e³-3) for all real t. If the position of…

A: The velocity vector in the xy-plane is for all real t. If the position of theparticle at , then to…

Q: - 16] [1] Determine whether the vector v =| 17 |is spanned by the vectors and | 2 or not. 18

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Q: Suppose the straight lines L₁ and L2 have respective vector equations 5 4 r1 = -3 + t 3 where s and…

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Q: Find the vector equation of the plane taking into account that 4x - y - z = 3

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Q: Find the projection of v = [-3, 3, 6] onto the line L with vector equation x=td where d = [4, -3, 1]

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