II1. Recall that using vector projections, we showed that the dis- tance from a point (x₁, y₁, 2₁) to a plane ax + by + cz + d = 0 is D |ax₁+by₁+cz₁+d Assuming that a, b, c are nonzero, give a different proof of this formula using Lagrange multipliers. √²+6²+c² =

Q: Choose a set S of three points such that aff S is the plane in R3 whose equation is x3 = 5. Justify…

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Q: 3. Find the Scalar eguation of the plane containing the line rt) =<!,2,-37+ -3,2, 17 and the point…

A: Given problem:- Find the scalar equation plane containing the line  r (t)= &lt;1,2,-3 &gt; + t &lt;…

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Q: Plane passing through point P0 (1, 2, 1) and perpendicular to vector (1, -1, 2) Find the equation…

A: Given:  Plane D1 : passing point P0(1, 2, 1)                 perpendicular vector (1, -1, 2) Plane…

Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: Find the value of k so that the line [x, y, z] = [2, -2, 0] + t[3, 5, k] is parallel to the plane 4x…

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Q: find the equation of the plane through P(1, 3, 2) that is parallel to the plane 5x - 4y + 3z = 7

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Q: If (x, y) and (X, Y) are the coordinates of the same point referred to two sets of rectangular axes…

A: and are the co-ordinates of the same point referred to the set of rectangular axes with same origin.

Q: Q7. a) Consider the vectors u , v and w are defined by u = i+j ,v = i+ 4j and w = 4i – 3j i. If the…

A: Given :

Q: e) Plane that is parallel to the xy-plane that contains the point A(2, 1, 3) (ca

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Q: 3. Determine the intersection (if any) of the following planes. Show your work clearly ₁: 2x + 3y z…

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Q: ind the equation of the tongent plane to fox,y)=x²-2xy + 2y ² slope 2 in the positive x direction…

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Q: (b) Let A(4,4, 7) and B(11,8, 11) be two points in 3D. Determine the coordinates of the point Q…

A: Introduction: When a vector is a non-zero scalar multiple of another vector, the two vectors are…

Q: II1. Recall that using vector projections, we showed that the dis- tance from a point (x1, Y1, 21)…

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Q: If the line x=1+(a+2)t, y=1-bt, z=-1+(c-1)t and the plane -x+2y-323D0 are orthogonal to each other.…

A: Given: Ratio of lineA^=&lt;a+2,-b,+c-1&gt; Ratio of planeB^=&lt;-1,2,-3&gt;

Q: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

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Q: 6. Determine the Cartesian (scalar) equation of the plane that... a) contains the points (6,1,0) and…

A: SOLUTION-