Find the orthogonal projection of y onto u. y = -3/5] - 4/5 /5 4/5 b) c) d) 2.

Q: ABCD is a plane quadrilateral and E is any point on AD. EF is drawn parallel to DB to meet AB in F,…

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Q: In AABC, X is the centroid. If CW = 15 , find XW. %3D

A: Given,           In △ABC, X is the centroid and CW¯=15

Q: If the plane ax+14y+cz=30 through the point P(2,3,−1) is orthogonal or perpendicular to the plane…

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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: If L is a line through 0 and if ŷ is the orthogonal projection of y onto L, then || ŷ|| gives the…

A: To state whether the given statement is true or false :  By definition, we know that, if L is a line…

Q: Let a = ci + j and b = 4i + 32j. Find c so that a and b are orthogonal. %3D i

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Show by Vector mothads that th ditonce hom fhe fornt P.(Xx, Y,, Z) to the plane Ax -+By+cz-D26 t of…

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Q: C, D are coplanar points. A', B', C', D' are their projections respectively on the y-

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Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in…

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Q: (b) Let the distance between two adjacent planes parallel to the plane (hkf) in the direct lattice…

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

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Q: Sketch the triangle with vertices at the origin O, P = (3, 3, 0), and Q = (0, 3, 3), and compute its…

A: The area of the triangle using the cross products is defines as Area=12v×u Here, v is the vector…

Q: Draw an obtuse triangle and, by construction, find the centroid of the triangle. (HINT: Begin by…

A: To get an obtuse triangle, draw a triangle with one of its interior angle should be greater than…

Q: Find the angles between the planes in Exercises 47 and 48. 47. x + y = 1, 2x + y - 2z = 2 48. 5x + y…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

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

A: Idea: if we project the surface in xy- plane z=0. if we substitute z=0 in surface equation we get…

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

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Q: 2. Given: WX = YZ; ZWXZ = ZYZX Prove: WXYZ is a parallelogram

A: Parallelogram

Q: The figure shows a parallelepiped spanned by vectors a,b and c Which of the following formulas…

A: The formula to calculate the volume is given by, Volume=area of base⋅height             =∥b×c∥ ∥a∥…

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

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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: In ANPQ, U is the centroid. If NS=15 find US. R S U

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Q: Let a = ci +jand b 7i + 56j. Find c so that a and b are orthogonal. %3D %D C =

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Q: The notation (x, y) → (-x, y) defines a reflection on the coordinate plane, O True O False

A: Solving the problem by helping of a point.

Q: The midpoint of AB is M(0, –4). If the coordinates of A are (2, –1), what are the coordinates of B?…

A: Given- The midpoint of ABis M0,-4. To Find- The coordinate of point B, if the coodinate of the point…

Q: Use the flux form of Green's Theorem to evaluate |(6xy + 8y°) dA, where R is the triangle with…

A: Greens' Theorem : Let D be the region bounded by the curve C. Let F(x,y)=P,Q be the vector field…

Q: Show there is no plane perpendicular to n=i+jn=i+j that passes through points P(1,2,3)P(1,2,3) and…

A: This is the rough image Point P(1,2,3) and Q(2,3,4) are the points on the plane…

Q: Calculate Se(5x + 3y) i + (4x + 3y) j) · dĩ where C is the circular path with center (a, b) and…

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Q: dA where R is the quadrilateral with the 5: Evaluate RI+y vertices (1,0), (4,0), (0,1), (0,4) using…

A: The solution are next step

Q: Let C denote the triangle with vertices at (0, 0), (0, 1) and (2, 1), oriented positively. Then f(x²…

A: We have to apply the green's theorem here.

Q: If L is a line through 0 and if f is the orthogonal projection of y onto L, then || F|| gives the…

A: Option B is correct.

Q: b. Describe the rigid motion(s) that would map AUVT onto ASVR.

A: Triangle SVR is congruent to triangle UVT by SAS congruence rule as per a. part. Four types of rigid…

Q: Evaluate by De Moivre's Theorem and express the result in rectangular form.(5e^j1.222)^2

A: De Moivre's Theorem: einθ=cosnθ+isinnθ →     *

Q: 7. If a =i+ 3j – k, b= 2i+ 4j – 2k and c = -i+2j+ 4k, find a number A such that d= a+b+ Ac is…

A: Given a=i+3j-k b=2i+4j-2k c= -i+2j+4k Find the  λ such that d= a+b+λc is parallel to the yz plane…

Q: Prove that the distance d from a point P (xo, Yo, 2o) to the plane r: Ar + By + Cz + D = 0 is given…

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Q: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.

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Q: Suppose we have: u = and v = . Based on their relative positions in the xy-plane, in which…

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Q: In space coordinates, the xy plane consists of all the points of the form O (0, y, z) O (X, y, z) O…

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Q: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

Q: If a? + b² + c² =1, then the distance from P (x0, y0, z0) to the plane ax + by + cz = 0 is |. |.…

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Q: Consider the projection from the origin of the straight line y + x = 2 on a straight line y + 2x =…

A: Graph formed by

Q: Prove that the shape ABCD is a rhombus. With A(1, 4), B(3, 0), C(1. -4) and D(-1,0).

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Q: Find a plane containing t and orthogonal to the pla

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Q: Find a plane that contains S and is perpendicular to the plane that contains the points

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Q: 3.4. For the standard coordinates uj = 0, u2 = Y on the sphere of radius a, compute the first…

A: Given: The standard coordinates u1=θ and u2=φ on the sphere of radius a.   To compute: The first…

Q: Find b such that B = (0, b) has hyperbolic distance of u from the point A (0,0).

A: Given: B=(0,b) has  hyperbolic distance of u from the point A=(0,0) Formula used:

Q: Use Green's Theorem to evaluate $4x²ydx+2ydy where C is the triangle with vertices (0,0), (1,2), and…

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Q: tor that is norma to the Plane determined by the three Points i+ 2j +k, si-j+ k , 3i + 2; - 7k.

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Q: Let D* be a parallelogram in the uv-plane with vertices A*(o)0), B*(를/듣), C*(를 ') E*( ).Let D be a…

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Q: 2. Show that AB CD + AC DB + AD BC = 0, given the points are collinear.

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