Which of the following represents a plane surfac whose x-, y-, and z-intercepts are a, b, and c respectively? 좀 + 음 + 등 1 C Ox +y+z = abc O ax + by + cz = 1 ||

Q: which of the toihts PC6,L3), Q (-5,-1,4), and R(0,3,8)15 c losest to the X2-Plane? which paint lies…

A: A point in 3D has (x,y,z) coordinates. A point on XY plane has (x,y,0) coordinates i.e. z=0 A point…

Q: 5. Write a rule for the translation of a point of the plane figure above. A. (x,y)→ (x-2,y+3) B.…

A: Translation of a point of the plane means moving all the points of that plane to a new coordinate.

Q: Let 6. 21 2 V2 = 4 9 For what value of h is y in the plane spanned by vj and v2? h =

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Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 15у — 12z — 2 %3D 0 (a)…

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Q: which one of the following pair of planes is parallel? 1. O x-4y-3z-2=0 dan 3x-9y-12z-7=0 2. O 1/4…

A: To find the pair of parallel planes

Q: Which of the following is the equation of a plane parallel to the cz-coordinate plane and passing…

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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: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

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Q: A plane in space contains the three points (2,1,3), (1,1,4) and (2,-1,3). Which of the following is…

A: Given points are (2,1,3) , (1,1,4) and (2,-1,3)

Q: The equation of the plane passing through the point A(8, 10, 9) and orthogonal to the line x = 7+…

A: Given: Point A(8,10,9) Line x=7+8t , y=6+4t , z=5+9t

Q: Find the distance from y to the plane in R spanned by the set {u1, uz} 4 - 3 -3 y = -9 -4 Uz 2 4 1…

A: Solution   Given,       Find the distance from  γ to the plane  in R3       spanned  by the  set…

Q: 4- Find The equation ofthe plane That the origin andat the poiat p(u1)ond at is parallel to theline…

A: Equation of plane

Q: Determine the value of K such that the points A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,K,-2) lie on…

A: Given A(4,-2,6), B(0,1,0), C(1,0,-5) and D(1,k,-2) AB→=(0-4,(1+2),(0-6))=(-4,3,-6)…

Q: Prove that the planes determined by the equations ax + by + c z = d and αx + β y + γ z = δ are…

A: Given planes, ax + by + c z = d αx + β y + γ z = δ

Q: Which of the following is the equation of a plane parallel to the yz-coordinate plane and passing…

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Q: Which of the following points is on the xy and yz planes, but is not on the xz plane? a) (2, 0, 0)…

A: We can represent 3D coordinate system.

Q: Show that the rank of the linear mapping 7.32. Bar Y3= 301 +302 y = 201 +20203, 31-02-203 1 V2 is…

A: To prove that the rank of the matrix (representing the given linear transformation ) is 2 and to…

Q: 0- Draw a sketch of the Plane of 4x-tyt22-9=0

A: Solution

Q: Determine whether the planes below are parallel, perpendicular or neither. 4x + 6y – 2z = 4 2x + 3y…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 23. Through (1,3, 5) and normal to7 - } +k.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (31) Find a plane through A(2, 1, –1) and perpendicular to the line of intersection of the planes 2x…

A: Given, 2x+y-z=3 ,x+2y+z=2 The equation of the plane passing through x1,y1,z1 is given by…

Q: Which of the following planes is parallel to the plane 3x – 2y + z= 3? - Oz=3x- 2y + 9 z = 6x- 4y +…

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Q: Determine the equation of the plane containing the points: P (1, 2, -3), Q (2, 3, 1) and R (0, -2,…

A: Vector equation of a plane passing through three points with position vector P→,Q→,R→is given by…

Q: Which of the following planes contains the z-axis?(a) z = 1 (b) x + y = 1 (c) x + y = 0

A: In 3 dimensions, the rectangular coordinate system has 3 perpendicular axes, x, y, and z. Any point…

Q: Find the symmetric equations of the L that is parallel to the two planes x+y-z= 2 and z + 3y+ z =…

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Q: Given: a plane containing the point P(-2, 5, -3) and the line [x, y, z] = [-1,2,5] + s[3, –4,1]…

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Q: is ndicular tò the plane containing the points: A = (-1,1, 2) B = (-3, 2, 1) C = (5 – 1, 1) the

A: Given that the plane is passes through the point A, B and C. We have to find the normal vector of…

Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3,…

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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: Find the distance from the point B = (1, 0, 2) to the plane P whose general equation is x + y -z =…

A: Equation of the plane is Given point is

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: Which of the following is the equation of the plane containing the points (2,1,2), (4,1,0) and (5,0,…

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Q: Find and describe the intersection of the following line and plane: T:2x+3y-4z =-7 and r = (4,2,5)…

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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: 11. Let a, =3 ,b3-5 For what value(s) of h is b in the plane spanned by a, and a2?

A: We have to find the value of h

Q: "Span(u1,..., in) = Span(71,..., Tn, w) if and only if J1,..., Un, w are linearly depen- dent."

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2) and…

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Q: Determine whether the planes are parallel or identical −x + 4y − z = 6, −(5/2)x + 10y − (5/2)z = 15

A: Given information: The planes are −x+4y−z=6, −52x+10y−52z=15. Calculation: The normal vectors that…

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

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Q: Which of the following is an equation for the line through the point (2, 3) and perpendiçular to the…

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Q: Find an equation for the plane in R® spanned by the points (1,5, 1) and (1, 4, 2).

A: We have to find the plane equation for two given points

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

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Q: Prove that the planes (i) 12x – 15y + 16z – 28 = 0, (ii) 6x + 6y – 7z –8 = 0, and (üi) 2x + 35y -…

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Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,-2) and…

A: To find the equation of the plane passing through the point P 2,2-2 and vertical to the line of…

Q: Determine whether the planes are parallel, perpendicular, or neither. 7x + 7y + 7z = 1, 7x – 7y + 7z…

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Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 18у — 15г - 2 %3D 0 (a)…

A: Given:   Equations is given

Q: Determine whether the planes are parallel, perpendicular, or neither. 2x – 10y – 8z – 1 = 0 (a) | -x…

A: Given problem:- Determine whether the planes are parallel, perpendicular, or neither.   (a) 2x…

Q: Find the intersection of the following geometric objects: the plane 3x - y + z = 3 and the plane 2x…

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Q: Find the point of intersection of the lines x = 2t + 1, y = 3t + 2, z = 4t + 3, and x = s + 2, y =…

A: Equate the x and y coordinates in t and s domain to obtain values for t and s.

Q: 4. Determine the general equation of the plane containing the points P(1, -4, –5), Q(2,0, 13) and R

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