(3.) The distance of two vectors x and y, dist(x, y) =|| x-y ||= / (x – y, x – y). (a) Find dist(r, -y). (b) Show that when dist(x, y) = dist(x, -y), then r and y are orthog- onal.

Q: Compute the angle between the vectors u = [2, 1, -2] and v = [1, 1, 1].

A: To find out the angle between two vector use the formula. First find dot product of these two…

Q: Find eguation of a Plane that an contains the vector: and and Z=3E

A:

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

A:

Q: Find two unit vectors that are normal to the plane determined by the points A (0, –1, 2),B (1,…

A: To find the two-unit vectors that are normal to the plane determine by the given points.

Q: Find a vector parallel to the line of intersection of the planes 2x + 3y – z =11 and 4x + 2y – 3z =…

A: We need to find a vector parallel to the line of intersection of the planes 2x+3y-z=11 and 4x + 2y -…

Q: Find a vector ū that is parallel to the yz-plane and perpendicular to the vector i = (0, 2, 2).

A:

Q: Find a vector v parallel to the intersection of the planes - (2x + 4y + 3z) = 4 and 3x + y + z = 7.

A:

Q: v, =,v, =, v, =

A: To add or subtract two vectors, add or subtract the corresponding components of each vector. For…

Q: Find a nonzero vector parallel to the line of intersection of the two planes – (2x + 3y + z) = -2…

A:

Q: Find a nonzero vector parallel to the line of intersection of the two planes 3y+4z=−3 and 5x+y+2z=4

A:

Q: 2 3 Let u and v %3D . Find the length of 2u and the length of -v. - Find the distance between u and…

A:

Q: Expreas the unit vector dirccted toward the point (0,0, A) from arbitrary point in the plane --2. an

A: In this question, we have to find the unit vector toward the given point from the given plane the…

Q: Find a vector function that represents the curve of intersection of two surfaces: z = x² - y? and x²…

A: Idea  1) Solve the equation in term of only one variable (2) assume in term of parametric function…

Q: 6. Find the distance of the point (-1,1) to the line given in vector form (x, y) = (2,0) +t(4, 3).

A: Given that: The point is (-1, 1).The vector is:  (x, y)=(2, 0)+t(4, 3)

Q: Verify the Pythagorean Theorem for the vectors u and v.u = (4, 1, −5), v = (2, −3, 1)

A: Given   The vector u = (4, 1, −5), v = (2, −3, 1) Pythagorean Theorem for the vectors

Q: . Value of t such that vectors a=, b=, c= are coplanar.

A: Value of t such that vectors a=<1, 1, 1>, b=<2, -4, 0>, c=<1, t, 3> are coplanar.

Q: Verify that the two planes are parallel. -x + 6y + 3z = 7 x+ 2y + z = 8 Find the normal vector, n,,…

A: Normal vector of a plane Ax+By+Cz+D=0 is defined as A, B, C

Q: A. If x and y are orthonormal vectors, then find the value of x+ yll- x-yll

A:

Q: Find a vector v parallel to the intersection of the planes - (x + 3y + 4z) = 7 and 2y – 2x + 2z = 7.…

A: The direction vector of the line of intersection of two planes is parallel to the cross product of…

Q: 19. Find two unit vectors perpendicular to vector u= (7, 0, -1) and vector v = (1, -1, 1).

A: We have to find the unit vector

Q: Find a vector v→parallel to the intersection of the planes 3x+y+2z=3 and       −(x+2y+4z)=7

A: Vector parallel to intersection of two planes is cross product of the normal vectors of the two…

Q: Vector v with initial point P1 = (x1, y1) and terminal point P2 = (x2, y2) is equal to the vector v…

A: Given : the two points are given as initial point P1 as x1,y1 and terminal point P2 as x2,y2.…

Q: -x + 6y + 2z = 6 1. -x + 3y + z = 7 2 Find the normal vector, n,, to -x + 6y + 2z = 6. n = 1 Find…

A:

Q: what is the distance between the vectors  u = (0,1,2,3) and  v = (1,0,4-1)

A:

Q: Let v =5j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane.…

A:

Q: Vector v with initial point P = (x1, yı) and terminal point P, = (x2, y2) is equal to the vector v =…

A: Initial point is P1=x1, y1 and terminal point is P2=x2, y2.

Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

A:

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

A:

Q: Find a vector perpendicular to the 2-space line: Qx - Ny + R = 0

A: Please see the below picture for detailed solution.

Q: Q2: Determined the component of the vectors at each point…

A:

Q: Let a be the angle between the vectors u=(-3,4,0) and v=(-4,3,0). Then

A: Given, the vectors u=(-3, 4, 0), and v = (-4, 3, 0).

Q: Q1-)A-) Find the distance from the point (0,1,1) to the line of intersection of the planes : x + 2y…

A: Given: A) Point (0, 1, 1) and the planes x + 2y + z = 1, x - y + 2z = -8. B) Vertices of triangle…

Q: find the vector equation of a plane that contains the intersection line of x + y + z = 1 and x – y +…

A:

Q: Find a vector v parallel to the intersection of the planes 3x + y + 2z = 3 and – (x + 2y + 4z) = 7.

A:

Q: 4. Determine a vector equation for the plane that is parallel to the xy -plane and passes through…

A: Due to our answering guidelines we can only answer one question at a time, therefore I will be…

Q: Compute the angle between the vectors u = [2,1, -2] and v = [1, 1,1].

A: Given: u=21-2   and   v=111 Formula Used: cosθ=u.vuv

Q: a nonzero vector parallel to the line of intersection of the two planes x + 3y + 5z = -3 and x + 3y…

A:

Q: Find the equation of the plane in xyz space through the point P= (3,3,4)and perpendicular to the…

A: We need to find equation of plane.

Q: Find a nonzero vector parallel to the line of intersection of the two planes 5y – 4x + z =-1 and –…

A: The line of intersection of two planes is orthogonal to their respective normals.

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

A:

Q: Find the equation of the plane in xyz-space through the point P = (5, 4, 3) and perpendicular to the…

A: NOTE: Refresh your page if you can't see any equations. . the normal vector is  . the given point…

Q: Verify the triangle inequality for the vectors u and v.u = (1, −1, 0), v = (0, 1, 2)

A:

Q: ) orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

A:

Q: 32. a) Determine the vector equation of the line of intersection of these 2 planes: x + 2y + 2z = -3…

A: According to Bartleby guidelines I can only answer the first question of the given two problems.

Q: Find a vector ~v ∈ R^3 such that ~v is orthogonal to the vectors (2, 3, −1) and (1, −2, 3) and ~v ·…

A:

Q: Let L be the line of intersection between the planes 2x +3y-z = 1, 2x 2y +2z = 5. (a) Find a vector…

A: The given planes are  2x+3y-z=12x-2y+2z=5 To find : (a) a vector v parallel to L Normal vector to…

Q: Verify that the two planes are parallel. -x + 6y + 2z = 4 -*+ 3y + z = 5 Find the normal vector, n,,…

A:

Q: Find a nonzero vector parallel to the line of intersection of the two planes 4x-2y+z=-1 and…

A: Answer

Q: Find a nonzero vector parallel to the line of intersection of the two planes 5z – (3x+3y) : 2 and 2x…

A: