2. Do the three planes X + 2y + z = 4, y - z = 1, x+ 3y = 0 have at least one commom point of intersection? Explain.

Q: Calculate gij for the distance between (x;) = (1, 1, – 1) and (yi) = (0,1,2) in %3D T-2 1] barred…

A: A point in three dimensional coordinate system is given by xi=1,1,-1yi=0,1,2 Now the point in barred…

Q: Find the angle of intersection of the plane 2x+3y+5z=−32x+3y+5z=−3 with the plane 3x+2y−1z=0

A: Given: - The plane is, 2x+3y+5x=-3, with the plane 3x+2y-z=0 To find: - The angle of intersection of…

Q: Find the area of the band cut from the paraboloid x2 + y2 - z = 0 by the planes z = 2 and z = 6.

A:

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

A:

Q: Verify that the two planes −x + 6y + 2z = 3,   −(1/2)x + 3y + z = 4 are parallel and find the…

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Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: 4 Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0, z+x3=0,…

A: Find the four vertices of the tetrahedron.  Making four equation.  Then write it in matrix form.…

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: Determine the location of a point (x, y, z) that satisfies the condition  ∣y∣ ≤ 3

A: If ∣y∣ ≤ 3 the point lies with in 3 units from xz plane on left side if y < 3 , or within 3 units…

Q: Are the planes 1/2 x + 2y − z = 5 and 3x + 12y − 6z = 1 parallel?

A: Given: Are the planes 1/2 x + 2y − z = 5 and 3x + 12y − 6z = 1 parallel?

Q: Are the following planes parallel or perpendicular or none? 3r+2y-5z – 9 = 0, 3x– y+2z – 9 = 0

A: Consider the given plane. The general for of the plane is defined as, A1x+B1y+C1=DAnd,A2x+B2y+C2=D…

Q: A sphere of constant radius r passes through the origin O, and cuts the axes in A, B, C. Prove that…

A: Given: Equation of the sphere with origin at O x2+y2+z2-ax-by-cz=0→1The radius of the sphere is…

Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

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

A:

Q: Determine the angle between the planes: x-z+7=0 2x +y-z+8 = 0

A: Solution :--

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

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

A:

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

A:

Q: 2. Do the three planes x + 2y + z = 4, y - z = 1, x+ 3y= 0 have at least one commom point of…

A:

Q: is the line x = 1 - 2t, y = 2 + 5t, z =-3t parallel to the plane 2x + y - z = 8? Give reasons for…

A: Given,

Q: 7x + 3y + 4z = 5, and 21x + 9y +12z = 13

A:

Q: Show thata perojective plane of gives 0nder indeed BİBD (+n+l, n+),1)

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

Q: A) Find the angles between the planes 2 x + 2 y + 2 z = 3 and 2 x - 2 y-z = 5

A: Given : 2x+2y+2z=3 and 2x-2y-z=5   To find: Angle between planes   we know that for plane Ax+By+Cz=d…

Q: Describe the intersection of the horizontal plane z = h and thehyperboloid −x 2− 4y 2 + 4z 2 = 1.…

A: Put z=h in given equation -x2-4y2+4h2=1⇒x2+4y2-4h2=-1

Q: Determine the location of a point (x, y, z) that satisfies the condition z = −5

A: The condition is z = −5

Q: 9. Find the angle between the two planes 2x + 3y + z = 3 and x + 3y + 2z = -3

A: Given,           2x+3y+z=3    and   x+3y+2z=-3We know that,           Suppose the two equation be…

Q: Prove that the distance between parallel planes with equations

A: Given : Two planes with equations n·x=d1 and n·x=d2

Q: A) Find the angles between the planes 2 x + 2 y + 2 z = 3 and 2 x - 2 y- z = 5

A:

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: 3. Determine the angle between the planes: x - z+7=0 2x +y-z+8 = 0

A:

Q: what is the intersection of plane  x+2y+z=0 and the line (x,y,z)=(0,1,2)+k(–1,1,2), KER(real…

A:

Q: Fud the Line pussing through the posnt (!,-l,o) and purrllel to the Eme of intersection of planes (X…

A:

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

A:

Q: 9. Suppose that a : R³ → R³ by perpendicular projection onto the plane 3x – 2y + z = 0. Find ↑

A:

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

A:

Q: The wedge cut from the cylinder, x2 + y? =1 by the planes, z = -y and z = 0. Set up only

A:

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: 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 (dis tan ant) between the planes ml and m2 when ml =: 3x - 2y+z = 9 and m2 =: 6x - 4y+ 2z =…

A: Consider the equation of planes m1: A1x+B1y+C1z+D1=0  m2: A2x+B2y+C2z+D2=0Two planes are parallel if…

Q: Find the acute angle (in degrees) between the planes x−4y−2z=1x-4y-2z=1 and −x+3y+z=−8-x+3y+z=-8.

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Q: and V is the dosed by the Planes x=0, y=O, ニこ

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Q: 8. What is the angle between the two planes x+y=0 and y-z=2?

A:

Q: What is the intersection of the plane x+2y+z=0 and the line (x,y,z) = (0,1,2)+ k(-1,1,2), kER?…

A: hello greetings from bartelby.i am here to help you.

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: What is the intersection of the plane x+2y-z=0 and the line (x.y,z) = (2,2, - 3)+ k(4,–1,1), kER?…

A:

Q: Evaluate JJ (² where o is the first-octant portion of the plane 2x + y + 2z = 6 (x² + 2yz)dS

A:

Q: Find the point lying on the intersection of the plane x + + z = 0 and the sphere x2 + y2 + z2 = 25…

A: According to the given information, it is required to find a point lying on the intersection of the…

Q: Suppose that II1 and II2 are parallel planes in R³, given by: II : ajx + biy +cjz = d1, and II2 :…

A: If ∏1: a1x+b1y+c1z=d1 and ∏2: a2x+b2y+c2z=d2 are parallel planes, then, the cross product ∏1×∏2=0.…

Q: Find the point lying on the intersection of the plane  x + (.5)y + (.25)z = 0  and the sphere  x2…

A: