Q. (x,BCTR. pMl Barel space AnB = $ HCAUBUC)= ? MLAUBUC)= HCAUB)a M(BUc)

Q: „Consider the space (R,T). where t={R,Ø}U{ACR:[0,1)CA} :Then (R,T) is not T, O T, but not T, O T2 O…

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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: Show that the volume V of a parallelepiped having u, v, and w as adjacent edges is V = ∣u ∙ (v ×…

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Q: Find mZH in rhombus GHIJ. 2x 3x+25° J %3D Submit

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Q: Determine las primeras derivadas parciales de la función en el punto (1,2) f(a, t) = V3x + 4t…

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Q: ind the valume of the portion of the Solid. Sphere x+y2,+2-10 that les between the Surfaces

A: We need to find the volume of the portion of the solid sphere x2+y2+z2 = 10 that lies between the…

Q: Prove that the volume of the sphere x² + y² + z² = a² is V =÷na³

A: In this question, we find the volume of sphere by using triple integral

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

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Q: Given that P l2 and PAP = D, compute A". %3D %3D

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Q: Find the volume of the parallelepiped having adjacent edges u, v, and w; for u = (1,-1,0), v =…

A: Given u=1,-1,0, v=0,2,2 and w=1,3,1

Q: A Find THE PERIMETER OF RHOMBUS ABCD WITH DIA GONALS AC AND BD INTERSECT AT poiNTE IF BD= 24 AND AC=…

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Q: Evaluate ſſ, Vy² – x² dA where boundary of R is the parallelogram bounded by the four lines

A: In this question, we evaluate the double integral by using the change of variable. The region is…

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

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Q: A(-3, 2), В(5, — 4), С(7, 7)

A: Consider the given points,  Now, prove that C is on the perpendicular bisector of segment…

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: A ve B ortogonal matrisler olmak üzere, aşağıdaki ifadelerden hangileri her zaman doğrudur? I.…

A: It is given that A and B are orthogonal matrices. The properties of orthogonal matrix are as…

Q: In the convex quadrilaterial ABCD the diagonals are perpendicular on one another, and they are equal…

A: A convex quadilateral ABCD. Diagonals AC and BD are perpendicular to each other and equal in length.…

Q: Prove that the midsegment of a trapezoid is parallel to the bases and its length is the average of…

A: To prove that the mid-segment of a trapezoid is parallel to its base, first consider a trapezoid…

Q: A space has the line element, ds? = v*du? +u*dv² . Determine whether this space is flat or curved.

A: It is given that the line element ds2=v2du2+u2dv2. it is required to determine that whether this…

Q: In right ARST (not shown) with right ZS, RV bisects ZSRT 6, ST = 6V3, and so that V lies on side ST.…

A: It is given that, ∆RST is right at ∠S and RV→  bisects ∠SRT so that V lies on  ST→ RS=6, ST=63 and…

Q: I, Use Stoke's theorem to evalueate S.Fidr, where F Cau2)= - it +x3 + 2î aind C is the Ceurve of…

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Q: Evaluate (image) over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 }

A: Given integral is ∭x2+y2+z2xyzdxdydz over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 } Change…

Q: What is the angle between the planes 3x + 2y + 4z = 4 and 3x -y+2z = 1 to the nearest degre %3D O…

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Q: Evaluate ry dr + r'dy, where C is the rectangle with vertices (0,0), (3,0), (3,1), and (0,1)

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Q: Show that the volume of a parallelepiped with sides A, B and C is given by A · (B × C)

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Q: of the fillowng Cuve. Aearly ntereepts on the axes O point of Inflechion

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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: Find the area of the parallelogram that has u = (1, 3, 0) and v = (−1, 0, 2) as adjacent sides.

A: Now cross product is,

Q: Find the stundand matices * and a for ToT,OT and て:→ド,1)- (-3y, fn + 3) T:→ド, 1.(4)): (J,)

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Q: Given NT bisects ZPNM, QS NM and NP RS. Prove that ZSON = LSRN HINT: show that quadrilateral NQSR is…

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Q: Find the orthogonal traiectories ofthe one-narameter fomilyy2 - v2

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Q: 3. Find the orthogonal trayectories to the cuve y = ax²- acx Is held fixed. 3 .2 %3D where a

A: The curves that cut every member of a given family of curves at right angles, is called an…

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: Evaluate ([(3xi +2yi)-d$ -d$ where S is a sphere x +y +z? =9.

A: To evaluate the below integral. ∫∫S3xi+2yj⋅ds Here S is a sphere x2+y2+z2=9

Q: Evaluate J CurIF. [cariF- nas F(x,v,z) = - yi + xj + zk, and S is part of the sphere z =9-x2 - y?…

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Q: The distance from (7,-8, 5) to yZ-plane is OA. 138 O B. 5 OC.8 OD. 89 O E. 7

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Q: 9. Name the figure that represents the two-dimensional cross section of the cylinder cut by the…

A: Given, A cylinder is cut by a plane  We have to name the figure that represents the two dimensional…

Q: find . In isosceles trapezoid HJKL, JK || HL. If mH = 450, JK= 6 cm, and the length of an altitude…

A: HJKL is isosceles trapezoid, so HJ=KL.Let the altitude is JP.

Q: These figures are congruent. What is mE?

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Q: Determine las primeras derivadas parciales de la función en el punto (1,2) (u, v) = z*y - 3yA O(1,2)…

A: Find the first partial derivatives of the function at the point (1,2) f(x,y) = x2y-3y4

Q: (b) Prove the volume of a parallelepiped with a vertex at the origin and edges ü,v, and w is given…

A: In the question we have to prove the formula.

Q: Find the envelope of the plane 1, C + u + a + и b + u mere u is the parameter.

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Q: 7. What additional piece is needed to prove JMLK is a rhombus ?

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Q: Prove analytically that the perpendicular bisector of the sides of a triangle are concurrent.

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Q: Derive the frenet frame, curvature and torison of the binormal indicatrix of hypocycloid?

A: We need to Derive the fernet frame, curvature and torsion o the binormal indicatrix of hypocycloid.

Q: Show that a indeed perojective plane of gives 0rder BİBD (n+n+,n+),!

A: We need to prove that a projective plane of order n indeed gives a BIBD (n2+n+1, n+1, 1)

Q: the dis fance from Pla.y,z) to the origion o d and fe clis fance from Pto ACo.003) is de .writeian…

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Q: Show that the sphere of radius 5, X(u, v) = (u, v, v25 – u? – v²) is regular.

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Q: y (b, f (b)) (a, f (a))

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