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

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

A:

Q: The acute angle of intersection of the planes x + y− 2z = 5and3y −4z = 6 is _____.

A:

Q: The distance from (9,-6, 7) to yZ-plane is A9 O B. 6 OC. 166 OD. 85 O E.7

A: Distance of a point (a,b,c) from yz plane is as In yz plane x coordinate is zero and y= b and z= c.…

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: Q1/ Find the angle between the planes 3 x -6y - 2z = 15 and 2 x +y– 2z = 5

A: Explanation of the answer is as follows

Q: 1 2x 3y + z = 0 and 2 +t - 1 1

A:

Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: 4. Find the angle made between the two planes: r+ y - z = 5 and 2r + y +3z = -1.

A: Given that: Equation of first plane: x+y-z=5   ........(1)Equation of 2nd plane: 2x+y+3z=-1…

Q: 5) Find the distances: a. Between l, = (2 + 2t, –1+ t,–3t) and l, = (4,–5 – 3t, 1+ 4t). %3D b.…

A: Given: (a). two lines l1 and l2 (b). Two Planes (c). A point (1,2,3) and a line  To Find: (a).…

Q: (42) is the distance between the point (1, –3, –2) and the plane x- 4y-3z-2= 0.

A: In this question we have to find the distance between point and plane. Note: As per our policy we…

Q: Find the acute angle (in degrees) between the planes Sz + 3y +5z 1 and 2z

A: P1 denotes plane 1 P2 denotes plane 2

Q: For planes 2x + y – z = 2 and 2x + 3y + 5z = 4,

A:

Q: Find the cosine of the angle between the planes x + y + z = 0 and x + 4y + 3z = 2.

A:

Q: Determine the distance between the given planes. π1 : −2x + 2y − 6z + 5 = 0 π2 : x − y + 3z + 8 =…

A: Given: Two planes are given Plane1: π1 : −2x + 2y − 6z + 5 = 0Plane2: π2 : x − y + 3z + 8 = 0…

Q: Q: To find an angle between planes 2x + 4y - 4z- 6 = 0 and 4x + 3 y+9=0.

A: We have to find the angle between the given two planes.

Q: Find the distance between the planes 5x - 3y + z = 9 and 5x - 3y + z = -6.

A:

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

A: Solution :--

Q: Find the line of intersection of the given planes. 4x + y + z = 0 and 2x -y + 3z = 2

A: Given planes are: 4x + y + z = 0 2x - y + 3z = 0 Let us consider, z = t Then we get, 4x + y = -t 2x…

Q: 7. Find the distance between the point (3, 1, –2) and the plane x + 2y – 2z = 4.

A: Given that plane x+2y-2z=4 and point 3,1,-2To find :Distance between point and plane Solution if…

Q: Find the line of intersection of the given planes. 3x + 2y + z = ~ 1 and 2x - y + 4z = 5

A: Given: 3x+2y+z=−1                                                      ...(i)2x−y+4z=5…

Q: Find the distance between the planes. 5x-2y+z-4 0, 5x-2y+z+6= 0

A: Given,  Equation of Plane 1: 5x - 2y + z - 4 = 0 Equation of Plane 2: 5x - 2y +z + 6 = 0 From the…

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Here, the given equation of the plane is 3x+y-6z=8 So, the coefficients of x,y and z will give us…

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: Find the condition for the points (a,0) ,(h,k),(0,b) when ab is not equal to 0 to be collinear

A:

Q: Find the distance between the given parallel planes. 4x – 5y + z = 16, 8x – 10y + 2z = 3

A:

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

A:

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

A: Angle between planes is defined as angle between their normals.    Option  C is correct answer

Q: Compute the angle between the two planes 2x + 3y + 7z = 2 and 4x - 2y + 2z = 4.

A:

Q: A plane can be determined by points, that are not on the same line. OA. unable to be determined OB.…

A:

Q: 5. Calculate the distance between the point (3, 1, -2) and the plane 2x + y-2+1. O 10 o -10 V14 O 10…

A: The equation of the plane is  2x+y-z+1 = 0 The point is x0,y0,z0 =3,1,-2 To evaluate : The distance…

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

A:

Q: x − 3y + 6z = 4 e 5x + y − z = 4

A: For the equation of plane a1x+b1y+c1z+d1=0, a2x+b2y+c2z+d2=0The angle between them is given…

Q: Find the distance between the given parallel planes. 2x - 3y + z = 8, 4x - 6y + 2z = 1

A: The solution are next step

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

A:

Q: Find the angle between the planes x+ y=1 and 2x+у-2z32?

A:

Q: Find the angle between the planes x+2y+2z-5=0 and 3x+3y+2z-8=0

A:

Q: Find the acute angle (in degrees) between the planes 5x + y + 4z = O and a y + 2z = – 3.

A:

Q: Find the distance between the given parallel planes. 2x - 4y + z = 8, 4x - 8y + 2z = 3

A:

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

A:

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: 12. Find the distance between the point (3,-2,7) and the plane 4x – 6 y + z = 5.

A: The equation of plane is 4x-6y+z=5 and the given point is 3,-2,7. The distance between the point and…

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

A:

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

A:

Q: 3. Determine the acute angle, to the nearest degree, between the planes T : 3x+ 2y - 4z +5 = 0 and…

A: π1: 3x+2y-4z+5=0comparing with Ax+By+Cz+D=0Direction ratios of normal=(3, 2, -4)n1→=3 i + 2 j - 4…

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

A:

Q: Show that line y+1 is parallel to plane x- 2y + z = 6 С.

A:

Q: Determine the angle between the following two planes: −x + 6y + 3z − 6 = 0 2x + 3z − 10 = 0

A:

Q: Find the point of intersection between the planes TT :x+y-z =1, n, : 2x – 3y -9z = 10 and n, : x +…

A: The three planes are, π1=x+y-z=1 π2=2x-3y-9z=10 π3=x+2y-3z=-4

Q: 17. Find the angle between two planes below. a. 2x- y+= =5 and 3x + y-z =1 b. 2x - 4y + 6z = 1 and…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.