Show that the plances x + y – z = 1 perpendicular. and 2x – 3y + 4z = 5 are neither parallel nor

Q: B. Show that line is parallel to plane x-2y + z 6

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Q: The point of intersection between the line t with the plane 2x + 3y +5z = 31 is

A: Given line ,x-1-4=y-13=z5=tTherefore any point on the line is of the form (1-4t,1+3t,5t)Put this…

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: Given: planes II₁ : 2x - 5y + z = −1 and II₂ : x + 5y + z = 5 intersecting on a line l (a) Compute…

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Q: Let P(x1, y1) and Q(x2, y2) be two points in the plane. Prove that the equation of the line through…

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Q: Show that the lines determined byr 1(t) = <−2 − 5t, 3 + 2t, 4t >andr 2(t) = <8 + 15t, 1 −…

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Q: What angle does the line of intersection of the planes 2x + y - z = 0 and x + y + 2z = 0 make with…

A: Given:The planes 2x + y - z = 0 and x + y + 2z = 0

Q: Show that the lines determined byr 1(t) = < 7, 3 − 4t, 2 + 6t> andr 2(t) = <6 − t, 3 + 8t,…

A: Given: r1(t)=7,3-4t,2+6t r2(t)=6-t,3+8t,9-5t For r1. x-7=y-3-4=z-26=t For r2. x-6-1=y-38=z-9-5=t…

Q: If 0 is the acute angle between the planes x + y = 2 and x + y +2z = 6, then 2cos (e) = O 1 O 1 O 2…

A: Given equation of planes are x+y-2=0 and x+y+2z-6=0 Let Let A1 x + B1 y + C1z + D1 = 0 and A2x + B2y…

Q: Find the distance between the given parallel planes: (a) 2x - 3y + z = 4 and 4x - 6y + 2z = 3 (b)…

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Q: The diagonals of rectangle QRST intersect at P. Given that mZPTS = 34° and QS = 10 , find MZSRT. %3D…

A: Find the angle SRT

Q: Show that the distance between the parallel planes                                          ax + by…

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Q: O Find the distonce from the point pC1,\, 1) to the plane 2K-3y+72=1

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Q: Show that the lines L1 : x =1– t, y = 2t, z = 4+t and L2 : x = 1+ 3t, y= 3 – 6t, z = 5 – 3t are…

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Q: If V = Ai - j +sk and Vz= 41+2j +4k, Find Value of (A) so that the length of Projection of V ont Vz…

A: Use the formula for length of projection of a vector onto another vector

Q: Verify that QR and MN are parallel. The length of segment MQ = 1.8, NR = 2, PQ =9 and PR =10. 10 1.8…

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Q: Find the eguatien of the tangett line and nemat plane to the cune; Y. cest Ces(zt)i + st sinCet) j +…

A: Given r=cost cos2ti+cost sin2tj+sintk

Q: Determine whether the plane x + y + z = 9 and the line x = t, y = -2t + 1, z = t + 2 are parallel,…

A: The given equation of line is in parametric form, x=ty=-2tz=t+2 Convert it into the cartesian form,…

Q: The diagonals of rectangle QRST intersect at P . Given that mZPTS = 34° and QS = 10 , find MZQRT . R…

A: From the given figure:   From the concept of the alternative interior angles:   ∠PTS=∠QRT.

Q: Show that the condition that the curves ax²+by²=1 a'x?+b'y²=1 1 1 1 1 Should intersect orthogonally…

A: If m1 = tangent at point (x,y) and     m2 = tangent at point (x,y) then Orthogonal conditions is…

Q: Find the distance between the given parallel planes. 2z = 2y – 6x, 3z = 1 – 9x + 3y

A: Find the equation by first converting both the equation as the parallel planes then find the answer.

Q: nat is

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Q: 4. Determine whether the planes are between them. 2x – 3y + 4z = 5; x+ 6y + 4z = 3 parallel,…

A: This question can be solved using the concept of angle between two planes.

Q: 8. Find the angles between the planes r+y = 1, 2x+ y – 2z = 2

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Q: If the four straight lines ax + by +p=0, ax + by +q = 0, cx + dy +r=0 (p-a)(r-s and cx + dy + s = 0…

A: The given equation of lines of parallelogram are  ax + by + p = 0,   ax + by + q =0 m1 = -a/b c1 = -…

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: If the four straight lines ax + by + p = 0, ax + by + q = 0, cx + dy + r = 0 |(p-4)(r-s) bс - ad and…

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Q: If the four straight lines ax + by + p= 0, ax+ by +q= 0, cx+ dy +r=0 |(p-g)(r-s)| and cx + dy + s =…

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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: A. Show that the planes (x+ y– z = 1 ) and (2x – 3y+ 4z = 5 ) are neither parallel nor…

A: let the normal vectors for the vectors be a1, a2 thus a1=<1,1,-1> and a2=<2,-3,4>. Let…

Q: Suppose that two lines Re((1+i)z+2i+3) = 0 and Re(2-bi)z+5) = 0 are perpendicular. then b=.

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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: 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: The diagonals of parallelogram WXYZ intersect at P. Which statement must be true? Select all that…

A: This problem is based on the properties of a parallelogram.  The solution is explained in step 2 in…

Q: 8. Find the angles between the planes r + y = 1, 2x + y – 2z = 2

A: We will use direct formula to find the angle. The detailed solution is as follows below:

Q: find the equation of the line through (0,2,1) that is perpendicular to both u= 4i + 3j − 5k and the…

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Q: Show that the line in which the planes x + 2y – 2z = 5 and 5x – 2y - z = 0 %3D intersect is parallel…

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Q: B. Show that line -- is parallel to plane x-2y+z = 6

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Q: What would allow you to prove AQRS = AXYZ by HL? R4 A ZQS = ZXZ B ZR ZY CZQ ZX D ZQ and X are right…

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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: If C is the line segment from (8, 4) to, (0, 0), find the value of the line integral: (6y? i + 5x})…

A: To solve the line integral from (8,4) to (0,0)

Q: Given that A and B are parallel to the yz plane, that |A| = 2, |B| = 4, and A • B = 0, what can you…

A: Consider the provided question, Given A and B are parallel to the yz plane.

Q: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Q parallel? Find…

A: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Qparallel? Find…

Q: Find the point on the plane 2x + 5y + z =9 that is nearest to (2,0,1). Vhat are the values of x, y,…

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Q: Let fiz) = x2 + iy? where x and y are the real and imaginary parts, respectively of z and C is a…

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Q: x + 4y + 2z = 4, and 4x -3y +4z = 7.

A: Topic - plane and vectors

Q: If the line L: X = 3 + 2t , Y= 2t , Z = t intersects the plane X+ 3y - Z =-4 in a point P. The…

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Q: ind the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y –…

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Q: Let f(z) = x² + iy where x and y are the real and imaginary parts, respectively of z and C is a…

A: ii