Given the following points in x-y plane: A(0,1), B(1,1), C(2,2), D(0,3), E(1,5), F(3,2), G(2,4), what is the unit vector parallel to vector FA? o/ -3/10 -V10 10 10 3 /10 (10 O (-3,1>

Q: Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R =…

A: We find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q =(4,-2,1)…

Q: Find a unit vector that is orthogonal to both u = (2, – 10, 8) and v = (4, 6, – 8).

A:

Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the intersection of this plane with the line…

A:

Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

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 the vector equation of the intersection of the plane x+2y+3z=2 and x+3z=3  r=<  ,  , 0…

A:

Q: If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, find the angle at…

A:

Q: Consider the vectors a = (-1,–2, 3), b = (3,0, –2), v = (2, –5, –4) and the plane P given by 2x + y…

A: The given vector is; a→=-1,-2,3b→=3,0,-2v→=⟨2,-5,-4⟩and Plane P is;2x+y=z+13⇒2x+y-z=13…

Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

Q: Which of the following vectors is orthogonal to the plane 3(x - 7) + (y + 8) - 5z = 15? O O O

A: Given equations of plane 3(x-7) +(y+8)-5z=15this is an equation of the form a(x-x1)+b(y-y1)+…

Q: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

A: Since r is the separation vector from the point x',y',z' to the point x,y,z and the difference…

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

A: Find your answer below

Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

A: RECALL: Orthogonal vector:  Let us consider to vectors a→ and b→ then , cross product of a→ and b→…

Q: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…

A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…

Q: Given A = x(2z -y) + ŷ(3x-2z) – 2(x+3y), find a unit vector parallel to A at point P =(-2, 1,–3).…

A: Vector valued functions are the rule that used to fix or associate a vector to a particular point…

Q: Find a vector that is orthogonal to the plane containing the points. (Orthogonal means…

A: Given points are, P=3,0,1Q=4,-2,1R=5,3,-1 The orthogonal vector n^ will be calculated from the given…

Q: Find a vector v that is perpendicular to the plane through the points А %3 (0, 4, —3), В 3 (5, —5,…

A: Coordinator of the plane is given Find out the vector that is perpendicular to the plane

Q: A plane contains the point  (1, -1,0 ) and its normal vector is \ vec {n} =  (6,24, -8 ). What is…

A:

Q: For what value of a is the vector v = ⟨4, -3, 7⟩ orthogonal to w = ⟨a, 8, 3⟩?

A:

Q: +C, vnere B 1s parallel to the vector (1, 2) C is perpendicular

A:

Q: Find a unit vector that is perpendicular to both ủ = (2,1, 2) and v = (2,– 2,– 1).

A: Given, u→=2,1,2 and v→=2,-2,-1 we are asked the unit vector that is perpendicular to both.

Q: Find a nonzero vector orthogonal to the plane through the points P, Q and R if P(1,0,0), Q(7,8,0)…

A:

Q: Find a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: Verify that the two planes are parallel. -x + 6y + 3z = 4 1 - x + 2y + z = 5 3 Find the normal…

A:

Q: Find a vector v that is perpendicular to the plane through the points A = (4, – 5, –2), B = (2,3,…

A: We are asked to find the vector that perpendicular to the plane through the points

Q: Find a vector v that is perpendicular to the plane containing 3 -() 6 and 0 2

A:

Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

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: 1. For what value of c is the vector v = = (2,–5, c) orthogonal to w = (3, 2,9)?

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

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given, A=( 1,1,0 ); B=( -2,3,-4 ); P=( -3,1,6 )To find: Distance from point P to the line through A…

Q: Given points P = (2,1,5), Q = (-1,3,4), R = (3,0,6), af Find the unit vector orthogonat…

A:

Q: Find nonzero vectors u, v, w that are perpendicular to (1, 1, 1, 1) and to each other.

A: Then   -------------(1) Also  --------------------(2)

Q: Consider the line L with vector equation (x, y, z) = (2,3,0) + t(1, 4, –1). Determine the point on L…

A: Foot of perpendicular is the closest point on the given line, Let M is the foot of perpendicular…

Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0) Which axis on…

A: From the given points we can find two vectors and after that, using the fact that if one vector is…

Q: Find a unit vector that is orthogonal to both u = (2, -8, 6) and v = (4, 10, -6).

A:

Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=&lt;2,-2,1&gt;.

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

A:

Q: 1 Which vector is perpendicular to the plane -2x + 3y – 4z = 9? 1 1 2' 3 О 2, -3,4] 2 1 9 3? О 12,3,…

A:

Q: Find a unit vector perpendicular to plane PQR. Р(1, -1, 2), Q(2, 0, — 1), R(0, 2, 1)

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

Q: What is the magnitude of a vector joining two points P(x1, y1, z1) and Q(x2, y2, z2)?

A: The two points  are : P(x1, y1, z1) and Q(x2, y2, z2). As the vector is directed from point P to Q ,…

Q: Which of the following vector is perpendicular to the plane 2x - 3y + 5z +7 = 0? O1-6, 1, 3] O [2, -…

A:

Q: Find a unit vector that is orthogonal to both u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩.

A: The given vectors are u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩. Compute the cross product of u and v as…

Q: Determine a vector equation of the line passing through (6, 0, 3) and parallel to the line of…

A:

Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on…

A:

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

A:

Q: Find a unit vector in the xy plane that is orthogonal 2 to 4 6

A: We have to find the unit vector.

Q: The surface of a hill can be given as h(x, y) = e-(z²+y²), If a ball is placed at the (2, y)…

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.