Find eguation of a Plane that an contains the vector: <-l,!,-1> and and Z=3E

Q: Show that the equation of a flat surface, represented in the Cartesian basis, is given by the…

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

Q: Find a unit vector that is orthogonal to both u and v for u = and v = .

A:

Q: The norm of the vector v= - i+10j-8k is ||v||=, (Round your answer correct to 3 decimal places)

A:

Q: Give a vector description of the midpoint M of a line segment AB.

A: According to the vector midpoint formula: Where 'c' is the midpoint position vector of vector 'a'…

Q: Find a unit vector normal to the plane containing v=2i+3j-k and . w = -2i - 4j - 3k.

A: Given: v=2i+3j-k  w = -2i - 4j - 3k.

Q: snip

A:

Q: Given Ā =,B = and C =. Find: a) the scalar projection of B onto C – À b) a unit vector ū in the…

A:

Q: Find a vector v such that v = 15 and v is in the same direction as –li + 13j

A: The solution is given as

Q: Find a vector parametrization of the line through P = (3, –8, 5) in the direction v = (-2, 0, 3)…

A:

Q: Find the B-coordinate vectors of ei and e2, where and B : %3D %3D %3|

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: Find the parallel projection of the vector v = onto the vector w=.

A: Given problem:- Find the parallel projection of the vector v=&lt;4, -5, 7&gt; onto the vector…

Q: [:] [] Find c so that the vectors and are parallel.

A: Find c so that the vectors c4 and 25  are parallel. Let u=c4 and v= 25 be two vectors. Two vectors…

Q: Find c so that the vector v is orthogonal to W = ||

A: Given: v=1c. w=2-1 Vector v and w are orthogonal only if the dot product of vectors is zero.

Q: IF A =2âx+4ây , B =-3âx+âz and C =2ây+3âz, the vector in the plane containing A and C and…

A: Given: Let us consider the given values as ,  A→,B→,C→A→=2a^x+4a^yB→=3a^x+a^zC→=2a^y+3a^z

Q: Prove the stated property of distance between vectors. d(u, w) &lt;= d(u, v) + d(v, w) for all…

A: We have to prove the property of distance between vectors as,

Q: Consider the vectors 'v (1, 0, 1) and w (2,0, -2). %3D (a) Are 'v and w perpendicular? (b) Show that…

A:

Q: Find the vector v of length 6 that has the same direction as the unit vector (1/2, V3/2).

A: Consider the following values: magnitude=6unit vector=12i^+32j^

Q: Consider the vectors 'v (1, 0, 1) and w (2,0, -2). %3D (a) Are 'v and 'w perpendicular? (b) Show…

A:

Q: Find the unit vector that has the same direction as the vector v. 31

A:

Q: Find the vector that makes equal acute angles with the positive coordinate axes and has length 2. O…

A: An acute angle is an angle that measure is less than a right angle (90 degrees). The magnitude of a…

Q: Consider the vector v = (−1, 3, 0, 4). Find u such that (a) u has the same direction as v and…

A:

Q: Find equation of Plane that an contains the vector: and 1-6 and Z=36

A:

Q: Let P be the plane in space that intersects the x-axis at 5, the y-axis at −5, and the z-axis at 4.…

A: Given query is to find the perpendicular vector to the plane p.

Q: For what value of t if any, is the vector 5t, 1] parallel to the vector (4, -1) ?

A:

Q: The vector is orthogonal to the plane 4x + 5y –7z =1 Select one: O True O False

A:

Q: Find a unit vector orthogonal to A in the plane of B and C if A = 2i - j + k, B = i + 2j + k, and C…

A: The given details are as follows.

Q: Find the value of c that will make the vector 2 lie in the span of 0 2 and

A:

Q: Consider the vector v = (2, y) in R?. If you rotate the vector by 90-degrees counter-clockwise, then…

A: Given,   v=2,y   in ℝ2.

Q: 16. Consider this regular octagon. If AB =d and BC =v, express each %3D vector in terms of u and v.…

A: Considering OD on x-axis. Angle at center O made by any side of regular octagon is 45degrees.

Q: 1Triangte with points (2.0r-)ornd R(or2 find -Ared of the iangle 7 vector PerPend teular to 2 AUnit…

A:

Q: ': Find all unit vectors parallel to the and perpendicular to the plane vector V = 5i -j + 2k

A: Here we find all unit vector parallel to the yz plane and perpendicular to the vectorv→=5i∧-j∧+2k∧

Q: Find a vector parametrization of line through P = (9, 8, 3) in the direction v = (4, -8, 6). %3D…

A:

Q: Given a vector Á = 3a, + 2a, + 6as , determine the vector component of Á perpendicular to the…

A: Topic:- vector

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = j, v = j + k

A:

Q: Find a unit vector that is orthogonal to both ı̂ +ȷ̂  and ı̂ +?̂

A: Given query is to find the unit orthogonal vector to the given vectors.

Q: Given a vector à = 3a, + 2a, + 6as , determine a vector that is perpendicular to A and tangential to…

A:

Q: The unit vector normal to the plane 2x + 3y + 6z = 7 is

A: The given plane is 2x + 3y + 6z=7. The unit normal vector to fx,y is defined as n=∇F∇F. The normal…

Q: Prove the stated property of distance between vectors.d(u, w) &lt; d(u, v) + d(v, w) for all vectors…

A: Basic logic and properties of vectors can be used to solve the question.

Q: Given vector A = (1, -2, xy), it can be said that vector A is uniform vector.

A: A=(1,-2,xy)

Q: B. Find a vector has length 10 in the direction of vector V=.

A:

Q: compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors. What do you…

A: Given: Compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors.

Q: Determine two unit vectors, vand wl, perpendicular to the plane passing through the z-axis and point…

A:

Q: Find unit vectors Parallel to the YZ Plaane and PerPendicular to the Vector V = 51-j+2k ?

A:

Q: What value(s) of a are necessary for vectors i = (2, a), and w = (4a, 3) to span R?

A:

Q: Assuming vector B is 12 units long, vector 4B is:

A:

Q: Give a vector description of the midpoint M of a line segment AB→.

A: GivenLine segment AB→To find vector description of midpoint of AB

Q: Which of the following planes are parallel to the vector (4, 1,-5)? Select one or more: O a. 6x + y…

A:

Q: Express in Cartesian components: (a) the vector at A(4, 40°, -2) that extends to B(5, -110°,2); (b)…

A: express in cartesian components (a) the vector at A4,40°, -2 that extends to B5,-110° , 2 (b) a unit…

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.