14) Determine whether u and v are orthogonal, parallel, or neither for u = <0, 1, 6> and V = <1, –2, –1>.

Q: Prove that if ||u|| = ||v||, then u + v and u- v are orthogonal.

A: Given ||u||=||v||

Q: The norm of the vector u = (1, 2, 3, 4) is 30. True O False

A:

Q: In Cartesian space, the direction of the line (x, y, z) = (a, b, c) +r(d, e, f) is represented by…

A: The given line is (x,y,z)=(a,b,c)+r(d,e,f) So, the point (a,b,c) is on the line and (d,e,f) is a…

Q: Determine whether u and v are orthogonal, parallel, or neither. u = (2,9) 2 O V= 32 parallel…

A:

Q: Prove that ||u + v|| = ||u|| + ||v|| if and only if u and v have the same direction.

A:

Q: Determine whether u and v are orthogonal, parallel, or neither.

A:

Q: Determine whether u and v are orthogonal, parallel, or neither. и%3 (0, 1,0), v %3D (1,—2,0)…

A:

Q: Show that there are no vectors u and v such that 11u 11= 1, ||v|| = 2, and uxv= 3.

A: If u and v are two vectors, and the angle between these two vectors is θ Then the magnitude of the…

Q: Show that if u and v are orthogonal, then || u * v || = || u || || v ||

A:

Q: Suppose that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

Q: Determine whether u and v are orthogonal, parallel, or neither u = ⟨−3, 0, 9⟩, v = ⟨1, 0, −3⟩

A: Consider the following vectors: u=-3,0,9v=1,0,-3 u¯·v¯=-3×1+0×0+9×-3=-3-27=-30 The two vectors are…

Q: Find u × v and show that it is orthogonal to both u and v.u = (2, −3, 1), v = (1, −2, 1)

A:

Q: If 7, r, and r, are three parallel vectors of the same magnitude Prove that i+r, +r, is equally…

A:

Q: Prove that for any vectors u, v, w , the set span{u+v,u – v, 3u – 3v + 2w} contains u, v, and w .…

A: A vector v is said to be contained in span of set S  (span(S)) if vector v can be written as a…

Q: Let y = #₁ = 1 and = 2 -27 -2 Write y as the sum of two orthogonal vectors, 1 in Span{u} and 2…

A:

Q: For any vectors u, v and w, show that uxv=uxw does not always imply v = w. Prove that u v ≤ ulv, and…

A:

Q: Verify that it is orthogonal to both a and b. (a × b) · a = (a × b) · b = %3D

A: Given

Q: Find u × v and show that it is orthogonal to both u and v.u = (−1, 1, 2), v = (0, 1, −1)

A: Given vectors

Q: Let u, v, w be three non-zero free vectors. Ju|2+ |v] + 23 |v|+|w| |u – v| + (v – u) |u +(v – w)| –…

A: The vectors u, v and w are non-zero free vector. u and v=magnitudeSo, u2=magnitudeMagnitude of a…

Q: Determine whether u and v are orthogonal, parallel, or neither.

A:

Q: Determine whether u and v are orthogonal, parallel, or neither.

A: We need to  Determine whether u and v are orthogonal, parallel, or neither.

Q: Determine whether u and v are orthogonal, parallel, or neither.

A:

Q: Determine whether u and v are orthogonal, parallel, or neither.u = (1, −1), v = (0, −1)

A:

Q: Show that u and v are orthogonal if and only if ||u+v|| 2 = ||u|| 2 + ||v|| 2

A:

Q: Determine if u = (4,3) and v = (1/2 , - 2/3) are orthogonal, parallel or neither.

A:

Q: Let u = (1,2,3) and v = (2a,2a,a2) Which of the following values of a ensures that u and v are…

A:

Q: Let u = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that u + v and w are…

A: Here, u=(1,2,3,4),v=(02,t,3) &amp; w=(1,1,0,1)

Q: Determine whether u and v are orthogonal, parallel, or neither.u = (0, 1, 0), v = (1, −2, 0)

A: Now dot product is, Since the dot product is not zero, therefore u and v are not orthogonal. Now…

Q: Let A, B, C be points in 3-space. Suppose that AB represents u, BC represents v, AC represents W.…

A:

Q: Determine if u = (0,3, -4) and v = (1, -8, -6) are orthogonal, parallel or neither.

A:

Q: Determine whether u and v are orthogonal, parallel, or neither.u = (0, 3, −4), v = (1, −8, −6)

A: u = (0, 3, −4), v = (1, −8, −6) We need to determine whether u and v are orthogonal, parallel, or…

Q: if u=(1,0,0) and v=(0,1,0), u and v are orthogonal Select one: True False

A: If dot product of two vector is zero then vectors are orthogonal

Q: Determine whether u and v are orthogonal, parallel, or neither. u = (2, 6) V = O parallel O…

A: The given vectors,    u=2, 6, v=32,-12

Q: 4 2. Detemine if v = and w= are orthogonal. Explain why they are orthogonal or why not. 3

A:

Q: ||u+ v|| = ||u – v|| if and only if u and v are orthogonal. Select one: True False

A:

Q: Suppose that u and v are vectors in 3-space such that |u||= 5 and u · v = 7.

A:

Q: Determine whether u and v are orthogonal, parallel, or neither. u = (9, -5, 4) v = (-1, 3, 6) %3D O…

A:

Q: Let y→=[−8, −7] and u→=[−2, 6]. Write y→ as the sum of two orthogonal vectors, x→1 in Span{u} and…

A:

Q: If an unknown vector X satisfies the relations X·b = β and X×b = c, express X in termsof β, b, and…

A:

Q: Determine whether u and v are orthogonal, parallel, or neither u = ⟨2, −3, 1⟩, v = ⟨−1, −1, −1⟩

A: Given: u=&lt;2,-3,1&gt;, v=&lt;-1,-1,-1&gt; To determine: Determine whether u and v are orthogonal,…

Q: Determine whether u and v are orthogonal, parallel, or neither. = (6, -6, 3) v = (-1, 2, 6) O…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: A- If P1(1,3, –2) and P2(4,7,-2) are two points. 1- Compute the length of 2P,P2 2- Is the vector…

A:

Q: 4.15. Given vectors u = and v =, find the projection of u onto v.

A: Proceed as shown below...

Q: 64. Show that if u + v and u – v are orthogonal, then the vectors u and v must have the same length.…

A: here, the given vectors, A =u+vB=u-v given that, they are orthogonal, that is, A·B=0u+v·u-v=0⋯⋯1

Q: Let

A:

Q: Determine whether u and v are orthogonal, parallel, or neither. u = (2, 27) (3 -) v = O parallel O…

A: u=2,27 v=32,-19

Q: If u, v, and w are vectors in R° , where u is non zero and u X v = u X w, then v = w. Select one:…

A:

Q: Determine whether u and v are orthogonal, parallel, or neither u = ⟨7, −2, 3⟩, v = ⟨−1, 4, 5⟩

A: Given: u=⟨7,−2, 3⟩, v=⟨−1, 4, 5⟩

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.