Find a plane containing t and orthogonal to the pla

Q: Find a unit vector normal to the plane containing v=2i+3j-k and . w = -2i - 4j - 3k.

A: Given: v=2i+3j-k  w = -2i - 4j - 3k.

Q: 3-Find the equatium uf tue plone that is parllel and at (& units) Aujay From The plane (x-ay+t=3)

A: The equation of the given plane is  x-2y+z=3

Q: Is the set c~(R* U {0}) “the entire plane without the non-negative reals" conformally equivalent to…

A: We need to evaluate the statement "the entire plane without non negative reals, ℂ-{ℝ∪{0}}, is…

Q: Find the projection of d on the plane P if a 4 and P has the equation x + y+ z = 1.

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Q: Find a formula for the projection of any given vector w onto the plane u · x = 0 in R', where u is a…

A: The objective is to find the formula for the projection of any given vector w onto the plane u.x=o…

Q: Let ABCD be a trapezoid with bases BC and AD. Let 0 = AB n DC be the point at which the lines…

A: Given that ABCD is a trapezoid with bases BC and AD, so BC and AD are parallel.…

Q: (A) Determine the plane that contain the point A(2,5,1) and the line L, t=x-2, 3t =y-1, t=z+1

A: The equation of the line L given in the parametric form, that is, Thus, the above equation of the…

Q: Compute the distance d from y to the plane in R' spanned by u1 and uz.

A: We have to find the distance d from y to the plane in R^3.

Q: d) If S is projected onto the x - y plane, what is the shape of the resulting projection?

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Q: For a plane with a normal of n = [1, 2, - 9]   and containing a point P (3, -4, 0), write the…

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Q: Determine the image of the upper half plane {z € C : Im(z) > 0 }

A: In this question, we use the transformation under g(z) we find the image set.

Q: Every triangle has a balancing point, called the centroid. O True O False

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Q: The half-space consisting of the points on and below the xy-plane

A: Concept:

Q: Let T be the plane x – y – z = 7. Which of the following planes are orthogonal to T and pass through…

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Q: Give another name for plane W

A: Plane :— Plane is a 2 - Dimensional space which is named by three Points.

Q: Suppose that AB is the diameter ofa circle with center O and that C is a point on one of the two…

A: Concept: The steepness of the line is called slope of a line. A steeper upward tilt to the curve…

Q: Show that the curve a(t) = (t,4,²) lies in a plane and find the equation of this plane.

A: Solution:- αt=t,1+tt,1-t2t t,1t+1,1t-t=x,y,z It is clear that, t-1t-1+1t-t=x-y+z x-y+z=-1

Q: Answer the following muitiple-chorce awestion belo alyebra #11. K is aveal nmber and e is the lime…

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Q: Let ū, and ūzare unique unit vectors normal to the plane containing a = 2i + 3j - k, and ,b =i-j+2k.…

A: Two vectors a and b in a plane are given. The vectors u1 and u2 are normal to the vectors a and b.…

Q: Prove that if r(t) has constant length, then r(t) is orthogonal to r'(t).

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Q: Let r() = (In1, 1, 5). Find the equation of the osculating plane corresponding to1 = 1.

A: Find the point at t=1 the vector r(t)=lnt,t,t22 corresponds. lnt,t,t22=ln1,1,122=0,1,12=0,1,0.5…

Q: What is the projection of r(t) = ti + t4j + etk onto the xz-plane?

A: Given: r(t)= ti+t4j+etk

Q: 24. Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in Figure 16, and…

A: The vectors v and w are in the x-z plane. The cross product of both vectors will yield a vector…

Q: . Consider a two-link planar robot ori- ented in the elbow-down position as shown in Fig. P3.26. If…

A: In this two-link planar robot oriented in the elbow down position, x=-1,y=15,l1=10,l2=8 The formula…

Q: Prove that the locus of the foot of the perpendicular drawn x2 +² a? = 1 to any of its tangent om…

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Q: Find the barycentric coordinates of p with respect to the affinely independent set of points that…

A: Given 11, 35, 06, p=23 let a=11, b=35, c=06, p=23 Now we write the points in augmented matrix form…

Q: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

A: Both vectors v and w lie in the y-z plane, which means they must have zero magnitude component along…

Q: Sketch the following Cartesian Products on the plane R? or in space IR. a. (-1,0, 2) x (1,2, 3) b.…

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Q: Compute the orthogonal projection of i = onto the line L through and the origin. proj, (1) =

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Q: Sketch the following Cartesian Products on the plane R? or in space {(x, y) € R²:x² + y² s 1} ×…

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Q: 12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is…

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Q: ) Find a lequabions for 6her line thirog gh Che porot (1,O.6) ond be the plane x t3y +2 -5- vecber…

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Q: 1 7 Let a, 4 21 and b = 6. 1 2

A: here we can use matrix method to write the equation of plane and then we use the condition that b…

Q: Find a parametrization c(θ) of the unit circle such that c(0) = (−1, 0).

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Q: Evaluate x2 zdS, where S is the part of the S plane z = 1+ 2x + 3y above the rectangle [0, 2] × [0,…

A: We have to evaluate ∬Sx2zdS, where S is the part of the plane z=1+2x+3y above the rectangle 0,2×0,3.…

Q: R) show that the pints ACI,l,4), B(2,2,2), c (o,1,5) and D(1,0,5) are coplanear (in the Same plane).

A: Form the three vectors and take the determinant of them. If determinant equal to zero it means all…

Q: 1. Find the three cube roots of z =-j and sketch the result in a single Argand plane. (express…

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Q: Find the projection of a on the plane P if a 4 and P has the equation x + y + z = 1.

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Q: In the following figure, there is a point labeled 1. Let a be the trans- lation of the plane that…

A: Given figure is

Q: Di+Oj

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Q: The part of the plane 3x + 2y +: - 6 that lies in the first octant

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Q: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

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Q: Let P be the plane with equation −x+2y−2z = 3. Find four distinct points on P at distance 3√10 to…

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Q: Let P be the plane 2r + u – 7 = 2 and let 0(1.0.3) be a poir

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Q: Sketch the following Cartesian Products on the plane R? or in space IR. a. {-1,0,2} x {1,2, 3} b.…

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Q: Sketch the following Cartesian Products on the plane R? or in space R. a. (-1,0,2} x {1, 2, 3} b.…

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Q: Find a Find a funds on the surdace 7=372y8 at which the feugend Planes is Parallel to the Plane…

A: We have to find the value of points on the surface