Consider the following subsets of the Euclidean plane R²: A = {(r.v) € R°| - 3

Q: of the tss plane passes threngh the point Cl,) and contains the line {x=t, Find the 9 =-2, 2= 2

A: According to the given information, it is required to find the equation of plane.

Q: 6. Find the intersection of the line / and the plane . 1:7=(4,-1,4) +t(5,-2,3) x: 2x+5y+z+2=0

A: Given is the equation of line as l:r→=(4,-1,4)+t(5,-2,3) Equation of plane as π: 2x+5y+z+2=0 First…

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: 6. Find a plane with the P (3, – 4, 5) and contains the line L:= =*

A: It is given that plane passes through (3,-4,5) and the DR's of a given line is 2,-3,5.

Q: 1. Do the following equations describe lines (L) or planes (P)? a) [x, y] = [1, 1] + s[2, 3] b) [x,…

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Q: Verify Green's theorem in the plane for M = -2y and N = x , where C is the semi circle x2 + y? = 9,…

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Q: Given is the plane V : a · x = 9 with a = (2, -3,6)t. Calculate the distance from O= (0,0,0) and…

A: Given that:The Plane  with To find: The distance from  and  to V.Concept:The distance d between a…

Q: by the equations { L₁ : X Y Let L₁ and L2 be lines in a 3-dimensional space given { = = Z = 3 + 2t…

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Q: Let a, -1 6 3 and b= -15 h For what value(s) of his b in the plane spanned by a, and a₂? The…

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Q: Let U₁= - 3. For what value of h is j in the plane spanned by ₁ and ₂? h V₂ = -9 [18] ý 11 -

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Q: Consider three points in three-dimensional space: A = (11,2, –5), B = (2, –5, 11), C = (-5, 11,2).…

A: Suppose P is a plane passing through a fixed point and a vector perpendicular to the plane or we…

Q: (a) (b) X = S y = t = 0 2 = x - 3 4 = −2+2 (c) x + y = 1 (d) x = 2y + 1 3 -3z + 1 4 || = 2

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Q: Q.5. D.] find the Cartesian equation of the plane r(u, v) (u,v + 2,3u-2v), -1≤u≤2 and -2≤0≤3

A: To find the cartesian equation of the plane from a given parametric equation, we need to eliminate…

Q: M3. Which of the following expresses the fact that the vectors u and v have the same length? (a) ū -…

A: M3. The two vectors u and v have the same length if: (a)u→·v→=v→·u→

Q: Let a₁ = 1 4 -1 a₂= The value(s) of h is(are) - 24 3 and b = 4 0 h For what value(s) of h is b in…

A: Given that: a1=14−1, a2=−7−243, b=40h To find the value of h if b is the vector in the plane spanned…