v₁ = (-1,2,1) ₁₂=(3, 1, 1) v₂ = (5,3, k) For which values of k a) {V₁, V₂, V3} spans 1R² ? b) ₂ 6 Span {4₁, 4₂} <) 1₂ € Span {√²₂₁, V;} d) v₁ 6 Span { V₂, V

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: What are the coordinates of P(23t/2)? А. (-1, 0) В. (1, 0) С. (0,1) D.(0,-1)

A: Solution

Q: The distance from the origin to the line passing through the points (0, 1,3) and (1,-1,2) is 14.

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Q: Find the cross product x where = 71-7j -4k and 7 = (-4,-3, 4). úxv=

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Q: solve For B, and B₂ 0 = -22 0 = = 2 2 i=1 Xii lyi - (B₁ Xii + B₂ Xiz)) x ₁₂ (y₁ - (B₁ Xi₁ + B₂ Xiz))

A: Given system of equations0=−2∑i=1nXi1(yi−(β1Xi1+β2Xi2))0=−2∑i=1nXi2(yi−(β1Xi1+β2Xi2))Which can be…

Q: For what values of h is v3 in Span{v1, V2, V3} ? Ta 2 -3, v1 v1 = 9. -7 -61 h

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Q: Find the cross product a × b where a = (0, 3, 4) and b = (5,1,2). axb =

A: Step 1: Step 2: Step 3: Step 4:

Q: 1. fCx)=メ?+6スープ (a) upward or downward? (6) axis f symmetry: x= le) verter C

A: Topic = Quadratic equation As per guidelines , at a time only three sub-parts can be answered.   If…

Q: ame: Date: 1. fx]=x +2x -X-2 2. x)=x-2x 8 Rel. Max Rel. Min: Rol. Mox Rel Min: Abs. Mox. Abs. Min.…

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Q: (2x) (4x+18)

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Q: Determine the points of intersection of  y=x^2   and   y=x+1

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Q: Which point(s) lie in the plane 2x + y - z = 10? a) (0, 0, 10) c) (2, 4, - 2) b) (5, 3, - 3) d) (-3,…

A: Given:plane: 2x+y-z=10

Q: The distance from (-3,-4,-7) to the xz-plane is (A) -4 (B) (C) -3 (D) 3 (E) 4.

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Q: Find Duf at P. f(x, y, z) = 6x³y³z³; P(2, — 2, 2); u = Duf = i + - 2|3 k

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Q: Use analytic geometry to classify the quadrilateral with vertices J(-2,1), K(2, 3), L(4, -1), and…

A: We have to classify the quadrilateral

Q: |(5z* + 3z*) (4x³ + 3x*)° dæ

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Q: Determine the length of x = 3+ (y – 2)², 4<x< 19

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Q: State the open interval where the graph is concave up. f(x) = - 6x³ - 36x² + 6x A) (-6,∞) E) (-2∞)…

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Q: What is the distance between points (0,0) and (-3,4)?

A: Given points are  We know that distance between the points (x1,y1) and (x2,y2) can be calculated by…

Q: Calculate the length of PQ where P = (-2,1,6) and Q = (-3,4, –1).

A: We will find the length of PQ→ in the following step

Q: If fxy (x, y) = , ,0 2) =

A: Given,fXY(x,y)=x+y27 ; 0&lt;x&lt;2 , 3&lt;y&lt;5

Q: Q2) Find the distance between the line y= - (x+2 ) & the center of the circle y + x – 4(x+ y )= 9

A: The center of the circle x2+y2-2ax-2by+c=0 is a, b Therefore, the center of the given circle…

Q: A 4,-1) B(4,-2) find lime x approachesto1 from postve dinection.

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Q: f v=[4,2,-3] what is dot(v,v)?

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Q: Let f(x)= 56-2) (x+1 What is the domain? b find all x-intercepts OFind y-intercept if it exists?

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Q: Q3) a) find f sec³ x dx

A:

Q: F(n) =3 Cn-2) C2n+2) Cn -7) For Funchon given 1) Determine the domain 2) Determine the range 3)…

A: Topic - domain ,range and intercepts of function

Q: Find the per pendicualar olistace from the P (5,6) to the line -2xr+3Y+4=0.

A: Formula for perpendicular distance is as below : Given :-2x+3y+4=0Ax+By+C=0A=-2B=3C=4 Point  (m , n…

Q: If f.(x, y) = 13x + 8y + 11, || f.(3, 2) = a. b. f„(5, 2)

A: Given, fx(x,y) = 13x + 8y + 11 a). fx(3,2) = 13*3 + 8*2 + 11 = 39+16+11 =&gt; fx(3,2) = 66