Hiw.2 Censider the PakullelePifed with šider: A=3i+2j+k Bziti+zkyczi+sj+3k;. thens t-Find the Volume-of the faralletefiped Find the area fthefacedetermined by Aand B. angle betweenthe Vector c and the plane containingthe face determined by A andB- 2- 3-Find the

Q: a) Find the acute angle in degree between the planes défined by 8x + 10y + 3z = 4 and 2x + 4y + 6z =…

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

Q: Which of the following is the volume of the parallelepiped determined by the vectors u=i+j-k,…

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Q: If a parametric surface given by r₁ (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -2 ≤ u ≤ 2, -3 ≤ v ≤…

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Q: Find the center and radius of the sphere x? – 6x – 8 + y? + 4y +z? – 20z = 0 OA C(3,-2,10), r = 11…

A: Recall: Equation of the sphere :         x-a2+(y-b)2+(z-c)2=r2; where a,b,c is the center and 'r' is…

Q: For what positive value of c is the acute angle between the plane containing the points A(0,0,1),…

A: The equation of the plane passing through the three non-colinear points x1,y1,z1, x2,y2,z2, and…

Q: Which of the following is not a parametrization of the parabola y = ² ? O x = vt, y =t O x = t, y…

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Q: 1. Consider the parallelepiped with adjacent edges u = 6i + 4j + 2k; v= 2i + 2j + 4k; w = 2i + 6k +…

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Q: If A = 18zî – 12j + 3yk then find SS,A.ñds where S is the surface of the plane %3D 2x + 3y + 6z = 12…

A: Given, surface S: 2x+3y+6z=12           and                       A→=18zi^-12j^+3yk^

Q: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

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Q: Determine whether the statement is true or false. If D is the disk given by x2 + y2 s 49, then 49 x2…

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Q: Determine whether the planes are parallel, orthogonal, or neither. 8x - 7y + z = 7 x + 2y + 6z = 1 O…

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Solution:-

Q: ? Find the surface area of the plane ( 15x-5z+20y%3D35) if it is in the first octant

A: Here we have to find the surface area of the plane 15x-5z+20y=35 ................... (1) for the…

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

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Q: Which of the following shapes could tessellate a plane on their own?

A: We know that triangles, squares and hexagons are the only regular shapes which tessellate by…

Q: Which of the following is the volume of the parallelepiped determined by the vectors u=i+j-k,…

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Q: If a = i + 3j j k, b = 2i + 4j j 2k and c = = i + 2j + 4k, find a number λ such that d = a + b + λc…

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Q: 1. Consider the parallelepiped with adjacent edges u = 6i + 4j + 2k; v= 2i + 2j + 4k; w = 2i + 6k +…

A: To answer the given questions using the given details.

Q: 1)calculate a*yz dædydz where D is the rectangular parallelepiped 1< « < 2,1 < y < 2,1 < z < 5

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Q: Find the equation of the plane which passes through O and is parallel (5а + бу) — 3 to z – %3D

A: The equation of given plane is,      z - (5x + 6y) = 3⇒ z - 5x - 6y = d   for a plane of the form ax…

Q: 4. If M is a centroid of triangle WOR and WM = 16, what is WX? %3D W Y M R

A: centroid:- i). It is the intersection point of all the medians of a triangle. ii). It divides the…

Q: Determine whether the planes are parallel, orthogonal, or neither. 9x - 2y + z = 3 x + 7y + 5z = 1 O…

A: We have to find the angle between the given planes which is equal to the angle between normals to…

Q: Calculate ff. (6 – z) dS if S is the cone portion z = limited by the plane z= 6 = 2/x² + y² Answer:…

A: Given the cone z=2x2+y2 limited by the plane z=6 At z=6, 2x2+y2=6x2+y2=3x2+y2=32 Thus, the…

Q: Find the distance (d) from the paint (9, 4, 6) to the plane z-y = 5. STAAVE

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Q: Determine whether the planes are parallel, orthogonal, or neither. 4x − 2y + z = 4 x + 6y + 8z = 1…

A: The direction ratio of the normal vector of 4x − 2y + z = 4 is (4,-2,1) The direction ratio of the…

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: B) Find the volume of the parallelepiped (box) determined by u, v, and w while: u = 10i + 20j + 50k,…

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Q: Зх + 2у + 3z %3D 6

A: Use a graphing utility to plot the graph of 3x+2y+3z=6 .

Q: Determine whether the planes are parallel, orthogonal, or neither. 8x - 5y +z = 6 x + 3y + 7z = 1 O…

A: We can solve the given problem as follows:

Q: Which of the following is the volume of the parallelepiped determined by the vectors u=i+j-k,…

A: The given vectors are u = i + j - k v = i - j + k w= - i + j + k To find volume of parallelpiped

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

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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: 4 Assuming that the curve ris thex + y +z = 0 intersection of the plane and the sphere , then the…

A: As per the question we are given a closed curve Γ , defined as the intersection of the plane x+y+z =…

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: If a parametric surface given by r1(u, v) = f(u, v)i + g(u, v)j+ h(u,v)k and –1< u<1, –2 < v< 2, has…

A: We will find out the required value.

Q: Determine whether the planes are parallel, orthogonal, or neither. 4x – 2y + z = 3 x + 5y + 6z = 1 -…

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Q: Given two lives (zt+l, st-s,lot) f (34, 2++3, z++1) loca ted in Side th plane ? (zt+l, 5t-5,lot ) f…

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Q: Which of these describes a parametrized line perpendicular to the plane 3x + 2y + z = 15? a)…

A: The direction ratio of the normal vector to the plane is (3, 2, 1) So the direction ratio of the…

Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…

Q: If a parametric surface given by ri (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -3 <u < 3, –4 < v<…

A: We solve this

Q: If A = 18zî – 12ĵ + 3yk then find Jſ, A.ñ ds where S is the surface of the plane %3D 2x + 3y + 6z =…

A: Note "As per our company guidelines we are supposed to answer ?️only first question. Kindly repost…

Q: Find feF- di utere Cisa crce of radus 2 in the plane z+y+ = = 9, centered at (2, 2, 5) and oriented…

A: The given function is, F→=2yi→-2xj→+3y-zk→ So, the curl of can be calculated as, curl…

Q: Determine whether the planes 2x − z = 1, 4x + y + 8z = 10 are parallel, orthogonal, or neither. If…

A: 2x-z=1,  4x+y+8z=10 Now comparing with a1x+b1y+c1z=d1  &amp;  a2x+b2y+c2z=d2, we get a1=2, b1=0,…

Q: Vhich of the following is the volume of the parallelepiped determined by the vectors u=i+j-k,…

A: volume of parallelepiped V =( u * v ).w

Q: Find the center and radius of the sphere x? – 6x – 10+y? + 10y +z? – 20z = 0 OA C(-3,5,10), r = 10…

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Q: Prove that the perpendicular distance from the point P(xo, Yo, 20) to the plane with equation ar +…

A: Here we use the distance formula between two points.

Q: The distance from a point S(xo, Yo, Zo) to a plane M: ax + by + cz + d = 0 is given by |n PS| d =…

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Q: Determine whether the planes are parallel, orthogonal, or neither. бх — 5y + z %3D4 x + 2y + 4z = 1…

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Q: x + 13y + 7z = 4, and 2x + 26y + 7z = 8

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Q: Determine whether the planes are parallel, orthogonal, or neither. 9x - 3y + z = 4 x + 4y + 3z = 1 O…

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