Let r = 2ji+yj+z¡k, r2 = ¤2i+ yzj + 22k and r3 = Lzi+ Yaj+ z3k be the position vectors of points P("1, Y1, z1), P2(x2, Y2, %2) and P3(13, Y3, 23). Find an equa- P. tion for the plane passing through P1, P2 and P3. See fig- ure on the right

Q: Determine the Miller indices of the plane that passes through three points having the following…

A: Given,     (a) (0, 0, 1); (1, 0, 0); and (1/2, 1/2, 0)  (b) (1/2, 0, 1); (1/2,0, 0); and (0, 1, 0)…

Q: Let P be a plane in space and let v be a vector. The vector projection of v onto the plane P,…

A:

Q: Verify that the two planes are parallel. -x + 6y + 3z = 8 1. x + 2y + z = 9 Find the normal vector,…

A: Let's find.

Q: Is the line x = 6- 3t, y = 8 + 8t, z= -t parallel to the plane 3x + y -z=2? Give reasons for your…

A:

Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in…

A:

Q: of the vector PP2• -ppositely direct to PP2 and whose norm is the doubl he same direction as PP.…

A: Consider the given point as, P11,-2,1 and P2-1,3,0

Q: Find the vector equation of the line of intersection of the planes x+y+z=1 and x+2y+2z=1.

A:

Q: Let M be a plane with the following properties: • M contains the point with coordinates (0,0,1) • M…

A:

Q: What is equation of the plane passing through the point A(-2, –1, –3) and parallel to the vectors ā…

A:

Q: Let r = ri+y1j+z¡k, r2 = 1zi+ Y2j + zzk and r3 = r3i+ yaj + z3k be the position vectors of points…

A:

Q: Which of the following describes a plane perpendicular to the vector n = (2, 1, -4) and contains the…

A:

Q: Let r¡ = r¡i+yj+z¡k, r2 = rzi+ Yzj+ zzk and r3 = rzi+ Yzj+ z3k be the position vectors of points…

A:

Q: Let P be the plane R3 with equation x+y-2z=4. the origin (0,0,0) is not in P! find two vectors in P0…

A: Given  x+y-2 z=4      .....(1)

Q: What is equation of the plane passing through the point A(2, 1,3) and parallel to the vectors a = j-…

A: We have to find the equation of plane passing through point A(2,1,3) and parallel to vectors…

Q: Let ri = xi+yıj+z¡k, r, = 1,i+ Yzj+ zzk and r3 = 13i+ Yzj+ zzk be the position vectors of points…

A:

Q: Let r, =1,i yj i z,k, r2 = 1ņi| jI zk and r=ại t vj t zk be the position vectors of points R(11, yı,…

A:

Q: Let the solid form in the orthogonal coordinate system xyz be surrounded by points A, B, C, D and F,…

A: The given co-ordinates of vertices are A = (-4, 1, 3), B = (6, 1, 1), C = ( 9, 5, 0), D = (4, 5, 1),…

Q: Consider the surface S given by: S: r(u, v) = (uv, u² + v³, 3v²), u € [0, 2], v € [0, 1] whose…

A:

Q: Write the equation for the plane. The plane through the point P(3, - 4,5) and normal to n= (5,5,5) O…

A:

Q: Define a basis B = (ā,b, c) for R³, where -- 2 6= 1 3 Define P to be the plane spanned by d and b.…

A: To define a basis B=a→, b→, c→, we determine the determinant of matrix formed by vectors a→, b→, c→.…

Q: Find the equation of the plane E passing through the point P(2,3,1) and parallel to the vectors K =…

A:

Q: Consider a plane in space that passes through the point (1, 3, 4) whose normal vector n is a…

A: The direction vector of given line is Therefore, normal vector to given plane is  We know that…

Q: Let ri = xji+yij+z¡k, r2 = x2i+ %3D %3D Y2j+ zzk and r3 = x3i+ Yzj + zzk be the position vectors of…

A: Vector equation of the plane passing through the points with position vector P1, P2 and P3  is given…

Q: Prove that the intersection line of the planes P₁: 2x -y - 2z = 0 and P₂:x-2y+z = 0 is parallel to…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: Let N = i − j + k. (a) What is the equation of the plane P containing (0, 0, 0) with normal vector…

A: a) The given normal vector N is 1,-1,1. The equation of plane is Ax-x1+By-y1+Cz-z1=0. Substitute the…

Q: The equation of the plane that passes through the point P(1,0,0) and has the vector n = (0,0, 1) as…

A:

Q: 3. Complete the following questions using the following planes T₂: 2x+4y-6z-2=0 m₂: 7x+14y-21z-7=0…

A:

Q: Let S be the plane defined by 5x-Sy+10z 0, and let T be the plane defined by 2x-2y+5z=-2. Find the…

A:

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 5z + 10 =…

A:

Q: 12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is…

A:

Q: Consider the vector y = [1 2 3]. Find the orthogonal projection of y onto the plane x, - 2x2 + 4x3 =…

A: Given vector is y=1,2,3 Given plane is x1-2x2+4x3=0 Normal vector to the p[lane is n=1,-2,4…

Q: Find a vector tangent to the curve of intersection of the two cyclinders ? + y² = 98 and y² + z² =…

A:

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y²…

A:

Q: Let M be a plane with the following properties: • M contains the point with coordinates (-1,-1,0) •…

A:

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A:

Q: Find an equation of the plane through the origin that is parallel to the plane 5x – 4y + 6z + 10 =…

A: Here we have to find the equation of a plane.

Q: Let ri = xi+yıj+z¡k, r2 = x2i+ Y2j + z2k and r3 = x3i+ Y3j + z3k be the position vectors of points…

A:

Q: Find a parametrization r(t,s) for the plane which contains the point P(-9, 7, 1) and the line…

A: Use plane concept

Q: Show that the vector V = (x+ 3y)i + (y – 32) j+(x – 2z)k is solenoidal. %3D

A: Solenoidal Vector : A vector function whose divergence vanished identically is called a solenoidal…

Q: Q5.Find a vector parallel to the line of the intersection of the planes 2x + y – 2z = 5 and. N, = 2î…

A:

Q: Find an equation of the plane containing the line a = 3t, y = 2 – 4t, z = 1+t and parallel to…

A: We have to find the equation of the plane containing the line x=3t, y=2−4t, z=1+t and parallel to…

Q: a) Find the distance between two skew lines L1 and L2 such that L1: 1+ 4t, y=5-4t, z=-1+5t  L2:…

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

Q: Let W be the union of the second and fourth quadrants in the xy-plane. That is, let W= Complete…

A:

Q: Which one is the unit normal vector of the plane spanned by Ä = 2î, – 6x, +2x, and B = 4x, + 3x, – î…

A: given vectors A→=2x^1-6x^2+2x^3 and B→=4x^1+3x^2-x^3 find the unit normal vector plane spanned by…

Q: Find an equation of the plane that passes through the point P(3, 5, 1) and has the vector n = (1, 8,…

A: As we know that; The equation of the plane which is passing through a point Px0,y0,z0 and a normal…

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 6z + 18 =…

A:

Q: Verify that the two planes are parallel. -x + 6y + 2z = 6 1 2t x + 3y + z = 7 Find the normal…

A:

Q: Find a vector parallel to the line of intersection of the planes 4х + 2y - 33 %3D17 and 3x - 4y…

A: Vector parallel to the Inter section of two planes  a and b is cross product of a and b Let m is a…

Q: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

A:

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.