dw dw Find ду at the point (w, x, y, z) = (- 4,1, - 1,1) if w = 4x y + 4yz - 4z° and x? + y? + z² = = 3. and ду

Q: M(3, 5) is the midpoint of PP2, where P has coordinates (0, 1). Find the coordinates of P2.

A: M (3,5) is the mid point of P1P2¯ , where P1 has coordinates (0,1).we have to find the coordinates…

Q: Q1, Find Paametric equations for the line through the Point (0,1, 2) that is U =i 12}+ 3k and ū= 3i…

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Q: a) Find the best straight line fit to the given data points (-3,7), (1,–1),and (3,–7). b) Find the…

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Q: Q.7: find the directional parametrization of the line segment joining two point A(2,1,3) and…

A: It is a basic questions of 3-D geometry , we have equate the equation only

Q: The distanced from P to the line l in R. D а b is given by |a x b| |a| d where Q, R are points on l…

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Q: Find (u+v).(2u-v) given that u.u=4, u.v=-5 and v.v=10 Determine if u and v are orthogonal…

A: Given, u·u=4, u·v=-5, v·v=10

Q: Q.1 Find the distance from the point P(1, -2, 3) to the plane 3x - 2y + z +1 = 0

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Q: Find parametric equations representing the line segment joining P(-4, 1) to Q(3, –2) as (æ(t),…

A: We have to find parametric equations to represent the line segment from P(-4,1) to Q(3,-2).

Q: GLet cons der the difterenti al equation us O gex) : e* is a so lution scx: (1+ x)e* is the andy so…

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Q: Q7) Find the angle between the planes 2x + y- 3z = 2 and -x + 2y - z= 1.

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Q: State Green's Theorem. Use it to calculate . ((13x – 5y)i + (13x + 5y)j) dr where C is the circular…

A: We will find out the required solution.

Q: Given ā(t) = (1, e¬t) and V(0) = (2,1) and F(0) = (1,–1) find the position elocity vectors. %3D %3D

A: Given a⇀t=1,et, v⇀0=2,1 and r⇀0=1,-1. To find the position and velocity vectors. Solution: We know…

Q: 2. Trapezoid QRST with vertices Q(3, 1), R(5, 2), S(10, 0), and T(4,-3); 270° counterclockwise about…

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Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

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Q: Show that u = au, + bu, – u + d, u=u(x,1) 4 is parabolic for a, b, d constants. Show that the…

A: The given second order PDE is                 uxx=aut+bux-b24u+d,  u=u(x,t)…

Q: Find the parametrization for the line through (-4,9) and (8, 13). (Use symbolic notation and…

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Q: The parametric equation of the segment [AB] with A(1,0,5) and B(3,1,2) is: O x-1+3t y=t z35+2t -<…

A: Two points A and B are given we have to find the parametric equation of the line segment AB. A line…

Q: Iculate | y?dx – yz²dy – sen(z)dz, where Cis the path connecting the point A(-2, 2, 4)to the point…

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Q: Yij - y = yij – J,. = yj - , + , -y. Given %3D | (Yj – y)? [(Yj – Y;) + Cỹ, – y) - - i. be

A: Given that…

Q: The parametric equation of the segment [AB] with A(1,0,5) and B(3,1,2) is: O x=1+3t y=t z=5+2t 0s…

A: Solution: Consider the given points are : A(1, 0, 5) and B(3, 1, 2) Parametric Equation of the given…

Q: F(6, 5) is the image of Kafter a reflection in the line y = 2. What are the coordinates of K?

A: Explanation of the answer is as follows

Q: Utt = C°AU in IR3 Schve the equations welve %3D with initieh dotes U0)= ¢()ー 0 Ut(8っ0)= Y(R)=X

A: The partial differential equation given is as follows: utt=c2uxx The initial conditions given are as…

Q: Q9) Find the angle between the line z +1 and the plane Zx + y + z – 2 = 0.

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Q: d. The plane through P,(2,4,5) perpendicular to the line x=5+t y=1+3t .

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Q: L:x= 2t, y= 2-t, z 2-t L2: x = 1-t, y = -3-t, z = 1-t M:x + 2y-z 3 straight in space and let's ha 1-…

A: The parametric equation of the line L1: x=2t, y=2-t, z=2-t L2: x=1-t, y=-3-t, z=1-t and the plane M:…

Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

A: I am attaching image so that you understand each and every step.

Q: (2t+l, st-5, lot ) f 4z: Given two lines ( 34, 2++3, zt+1) located in Sice the plane ? plane, find

A: The required equation for the plane is calculating by the below method.

Q: (s) (a) Find a parametric equation for the line through (2, 4, 6) that is perpendic- ular to the…

A: Equation of line in 3D

Q: In ARST, SV bisects y ZRST. Find the coordinates of point T in terms of a. S (a, a) 2a T?, ?) V (2,…

A: Given that, Let ∠TSV=θ and ∠VSR=θ(∵SV is angle bisector)

Q: Parametrize the directed line parabolic segment y = x2 that joins 2 + 4i to −1 + i.

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Q: For vectors a and b in R² prove Lagrange's identity: ||a x b||? = ||a||2||b||? – (a · b)? ах

A: Use the vector product and scaler product identity, a×b=absinθn^…

Q: Plot the points on the same three-dimensional coordinate system. (a) (3, 4, 1) (b) (-2, 3, 7) 10. O…

A: Given Data: Plot the points on the same three dimensional coordinate system. (a) (3,4,1) (b)…

Q: Find a parametric description r(t) for the ine segment from (-1,-3,-1) to (1,7,4). Provide your…

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Q: The distance between the two lines x = 1+ t,y = -2 + 3t, z = 4- tand x = 2s, y = s, z = s is a) 1/2…

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Q: lo. find a point in the plane x+2y+3z=13 nearest to the point (1,1) usung the methed of Lagrange's…

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Q: t u - (1,1, -2) аnd v = (a, –1, 2). For what values of a are u and v orthogonal?

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Q: Hx.y)=Vtanlx)+y and u is the wit etor in the direction find U IS 6)DE(-04,7) - a.d,7)=Dy F(-a.l,7)=…

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Q: 3. Find the acute angle between the lines. x - 1 3 - y z+5 (a) l1: 3 (b) l1: r = 7 – 2t, y = 4+3t, z…

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Q: giren points wll, 2), x (4,-3), y (-6, +) and z (-4, +) cartesjan plane on Since tnow that A Cb), B…

A: To find:- How opposite and adjacent sides related to given slopes  And What specific geometric…

Q: ue or False. Let x, y E R". If || + y = ||x – y||, then x cannot be orthogonal to y.

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Q: a = i+3j- k, 6= 31- j+ k, d = -31- j+ k, j = i+3+4k. č = 3i+j+4k %3D perpendicular to b and c, enter…

A: If we have to find the vectors to be perpendicular then their dot product should be 0. The formula…

Q: Find the parametric equation of line that passes throught the point (1,-2,4) and is parallel to the…

A: The given point is (1, -2, 4) and parallel to the vector v=[2, 4, -4].

Q: Find T, N, and B for the curve r(t) = (41, 4t, e' ) at (0,0, 1). Hint: After finding T', plug in the…

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Q: Find parametric equations of the normal line to *+ y? at the point (2, 2, 5) the surface z = O = 2+…

A: A detailed solution is given below.

Q: Find parametric equations for the line segment from  (9, 2, 1) to (5, 5, −1).  (Use the parameter…

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Q: alculate y'dx – yz²dy – sen(z)dz, where Cis the path connecting the point A(-2, 2,4)to the point…

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Q: A sufuce S contains 2. r2(u) = (2u^2, 5-u, 6+2u) Find an equation for the tangent plane to S at the…

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Q: Suppose F(x, y) = x?i+ y?j and C is the line segment segment from point P = (-5, –5) to Q = (-3,…

A: Given data: The given expression for the vector is F→(x,y)=x2i→+y2j→. The given first point is…

Q: 17. Find the angle between two planes below. a. 2x- y+= =5 and 3x + y-z =1 b. 2x - 4y + 6z = 1 and…

A: