X/ Find The normal vector to A = 2i-3j+4K , B = i-2 j+ 5K AxB=Ñ =? ĀXB=N -3 4 = -7i-6j-K %3D - 2 Hw/ prove À tÑ, 12

Q: Write down the equations of any two distinct planes with normal vector n = 〈3, 2, 1〉that do not pass…

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Q: 436. The plane that passes through point (4, 7, -1) and has normal vector n= (3, 4, 2)

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Q: Find linearly independent vectors which generate al lutions of Ax = 0.

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Q: Find the normal vector to plane y-x-2=0

A: A unit vector is a vector of length 1. Any nonzero vector can be divided by its length to form a…

Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

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Q: A. If x and y are orthonormal vectors, then find the valne of x+ yl? - |x-yl

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Q: e modulus valu

A: In the given question, the concept of derivatives is applied. Derivative We can use a derivative to…

Q: The divergence of the vector G = 2i+ sin y j+ 3k is :- -8y + x3 -8y siny + cosy O Option 3 O Option…

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Q: Find the components of the vector whose initial point is (2, 2, 4) and terminal point at (0, 2, 0).

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Q: Find the terminal point of a vector v = with an initial point P(0, 6, 2).

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Q: XII. Show that the dual vector of the antisymmetric part of the dyadic (1 2 3) A = 4 2 1 1 1 1) is…

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Q: The normal vector of x+2y-1-0 (0, 2) (2, -1) (1, 2) O (1, -1)

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Q: The divergence of the vector G=i+siny j + 3k is :- -8y x3 + siny -8y x3 + cosy Option 1 Option 3…

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Q: Find an equation of the plane through the point (4, 5, 1) and with normal vector 6i + j - k. Show…

A: The plane passing through a point A(a) with the normal vector n is given by: r·n=a·n where,…

Q: Find a normal vector at point P. xy2 - 4x2 + y + 8x = 7, P(4, 3) Find a tangent vector at point P.

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Q: Calculate the integration of (A" - dlP2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector…

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Q: Find an equation of the plane through (1, −3, 5) with normal vector n =〈2, 1, −4〉.

A: Consider the given: Point on the plane is P = (1, -3, 5) Normal vector to the plane is n→=2,1,−4 Let…

Q: Use the full differential to calculate an approximate modulus value. of the vector (5, 8 ; 3, 1 ; 2,…

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Q: Write the scalar equation of the line given the normal vector n =[1,−1] and a point Po (-5,1)

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Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

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

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Q: Compute the normal vector to the surface Ф(и,0) %— (и? — 0?, и +0, и — 0) at that point (4,3).

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Q: What will happen if the Gram–Schmidt process is applied to a set of linearly dependent vectors {v1,…

A: Introduction: The Gram–Schmidt system is a way for orthonormalizing a fixed of vectors in an…

Q: 46. The plane that passes through point (4, 7, -1) and has normal vector n = ( 3, 4, 2)

A: This question can be solved using the concept of equation of plane passing though a point and…

Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

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Q: why you write: s=0, t=0 s=1, t=1  instead of using cross product imediately between 2 vectors…

A: The vectors (1, 0, 1) and (1, -1, 0) are direction or orientation vectors. The cross product of…

Q: Find basis for the set of vectors in R2on the line y=nx. where n is last digit of your arid number.…

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

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Q: What will happen if the Gram–Schmidt process is applied to a set of vectors {v1, v2, v3}, where v1…

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Q: Find an equation of the plane that passes through the point P(-8, –4, 7) and has the vector n = (-2,…

A: Given problem:- Find an equation of the plane that passes through the point P(-8, -4,7) and has the…

Q: XII. Show that the dual vector of the antisymmetric part of the dyadic (1 2 3) Ā = 4 2 1 (1 1 1) is…

A: 1st calculate the antisymmetric part of the corresponding Tensor (matrix form). Then apply the…

Q: ind The normal vector to The vectou zi-3;+ 4 K so/ There is 0 numberof vectors.lin spaci).

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Q: 18 as a linear combination of = 8 Express the vector i and j =

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Q: Find an equation of the plane containing the point P(2,1, –1) and having the normal vector N = -î+3…

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Q: Find the stable vector of P || -

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Q: 2 3. Show that that the vector u =|-5 is a linear combination of the vectors vi = -4 and vz = 3.

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Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

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Q: 6.) Find a vector equivalent to the vector PQ with its initial point at the origin. = (;-2), Q =…

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Q: Is the set of the three vectors S linearly independent? Explain why. S = 2

A: From the definition, a set S=v1,v2,v3 is said to be linearly independent if the linear combination…

Q: b) Express the vector (–1,5, –6) in R³as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

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Q: 3. Show that that the vector u = -5 is a linear combination of the vectors vị = 3 U2 = and v3 %3D

A: Given vectors are u=   2-5  3, v1=  1-3  2, v2=  2-4-1 and v3=  1-5  7   To show that u is a linear…

Q: Consider the vector v = 2t2 + 1 1 (2t, 2t², 1) . The derivative of v with respect to t is (2 – 4t²,…

A: Using the quotient rule of differentiation, it can be written as follows. ddxxy=ydxdy-xy2

Q: A particle starts moving from (- 4, 2, 5) so that its initial velocity is 5 î -3 ĵ – 2k and its…

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

Q: State the Cauchy-Schwarz Inequality and use it for solving the two vectors in R³ if = [1,–2,4] and y…

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Q: 4. Find an equation for the plane through (1, 3, 4), with normal vector .

A: topic- equation of plane with point and normal vector

Q: Find two orthogonal vectors in the plane x + y + 2z = 0. Make them orthonormal.

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: -) Are these pairs of vectors orthonormal or only orthogonal or only linearly independer [:]; » [] 1…

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Q: ind a vector orthogonal to both u and j+k. u=2i-j+3k

A: we have been given two vectors,  u = j+k. v=2i-j+3k   the unit vector that is orthogonal to both…

Q: 200 400 300 If the components of stress at point p given by 400 0 Mpa. 300 0 -100 then the stress…

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Q: The normal vector of 2x + 3y - z + 5 = 0 is: O [3, -1, 5] O [2, 3, -1] [2, 3, -1, 5] O (-2, -3, 1]

A: Answer :  From question given that the Normal vector form is  ; 2x + 3y - z + 5 = 0

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.