3, Four- vectors and Yy in the Schwarzschild space time Ne giver as %3D a) Find the covariant vector Xx b) Find the contravariant vector y*

Q: 7. Find an initial point P of a nonzero vector u = PQ with ter- minal point Q(3, 0, –5) and such…

A: We have to find an initial point P of a non zero vector u = PQ→,  with terminal point Q(3, 0, -5)…

Q: Inside Rn , suppose dimension (V) + dimension (W) > n. Show that some nonzero vector is in both V…

A:

Q: 3 Among all unit vectors u = y in R', find the one for which the sum x + 8y+ 4z is minimal.

A:

Q: What is the unit vector perpendicular aial yA n = i-j+ 3k, n2 = 2i + j + 3k to the vectors?

A: Given that:n1=i-j+3k,  n2=2i+j+3k

Q: The value of the chiral vector of SWNTs if the n=8 , m=6 and the first vector length equal n/2+1 and…

A: Given that m=6,n=8to find the chiral vector of SWNT.  As we know that, the chiral vector c can be…

Q: of the vector PP2• -ppositely direct to PP2 and whose norm is the doubl he same direction as PP.…

A: Consider the given point as, P11,-2,1 and P2-1,3,0

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

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Q: Solve numerically for The scalar projection of vector u onto v

A:

Q: find a vector parametrization for the line with thegiven description. Passes through (1, 1, 1) and…

A: The vector parametrization is:                                       r(t) = r0 + tv = x0,y0,z0 +…

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: Consider the Vector-Valued Funcbion く os6) +ド いnct), Cosit)+4 5inct,-20 Ginco since) 015 a Compute…

A: We are given with vector r ;

Q: Find a-Vectak S unit, tengte inthedirectionofthe Vector A-ixjtk-

A:

Q: 4

A: We are given the following vectors.

Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar proju(v + w) or vector.

A: Here given vectors as u = -i + j, v = 3i - 2j, and w = -5j. Thus  v+w=3i-2j+-5jr(say)=3i-7j

Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: Two vectors Px1,y1,z1 and Qx2,y2,z2 Line segment P to Q: 1) Parametric form is…

Q: Find the projection of vector w = onto vector v = . Round all components to the nearest hundredth.

A:

Q: The vector a in 3-space of length 3 lying in the yz-plane pointing upward at an angle of 5π/6…

A: let w= aiÌ‚ + bjÌ‚ + ckÌ‚   |w|= a2 + b2 + c2 = 1   W is lying in YZ plane and at an angle of 5π/6…

Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: we have to represent the line segment from P to Q by a vector valued function and by a set of…

Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

Q: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: If the vector K az+Lay+ Ma, shows the maximum increase rate and direction of the scalar V at point…

A:

Q: Make all obvious simplifications.

A: We have to solve

Q: Find two different vector parametrizations of the line through P = (5, 5, 2) with direction vector v…

A: Given the points are (5,5,2) and the direction vector v=&lt;0,-2,1&gt;Hence, Vector…

Q: () 1 (b) Find the length of the component of the projection of the vector a = vector 6 = 2 () onto…

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Q: 1 Find two vectors of norm 1 that are orthogonal to the vectors u = and v = 3

A: Given problem is :

Q: 18. Find the vector u in 2-space of length 2 that makes an angle 0 4.

A: A vector having length u→ and makes an angle θ is given by  u→ = u→cosθ i^ + u→sinθ j^

Q: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

A:

Q: 10) (6 points) Using the inner product (v, w) = 3v¡W1+5v2W2 with the vector space R?. a) Find a…

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Q: 26. Find a unit vector whose representations are perpendicular to the plane containing PQ and PR if…

A:

Q: 2. If A is the position vector of the point p-(x,y,z) and A=A. And ifr is the radius of the point in…

A: We apply the cross product to find the given function and simplification needed.

Q: 2. Which does not exist for a line in three-space? a) vector b) parametric c) symmetric d) scalar

A:

Q: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

A: Let u and v be tthe vectors in 3-spaceThen by Lagrange's identity,we haveu×v2 =u2.v2-(u.v)2…

Q: A vector t has initial point (0, 0) and terminal point (4, 1). Write t in component form.

A: Write vector, terminal point minus initial point

Q: Find the weighted Euclidean distance between the given vectors. -- - - u = 3 with weights w = d(u,…

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Q: Express the vector H %3D p?za, + зфzaф - рф*а, at B(3, -4, 1), in CCS.

A: The given vector is H→=ρ2z aρ+ 3Φz aΦ - ρΦ2 aZ.We have to express it in the cartesian co-ordinate…

Q: 1. Do the vectors 日 span R (over R)? Justify your answer (using methods and results that we have…

A:

Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

A:

Q: 1. Compute the angle Pair Of vectors in Standard inner producy on Mzz. between tre following Mzz…

A:

Q: Let u = -2i + 3j, v = 6i - j, w = -3i.Find specified vector 4u - (2v - w)or scalar.

A: To Determine: find 4u-2v-w Given: we have u=-2i+3j  ,v=6i-j  ,w=-3i Explanation: we have…

Q: 1. The path of a partide i3 qiven by Sut) =<3 lose, a thint 7 find a) Velouity vector and…

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Find a unit vector u in the direction of v = 〈6, -1〉. Verify that ⎥⎥ U⎥⎥ = 1

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Q: -2 - are the vectors U, = %3D Ug = %3D in M22 are lineor ly depon dent linearly in dependet.

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Q: In Cartesian coordinates, a rank-2 tensor is given by Į = Tr£xx + Tvz£xz+ Tyy£yy and a Cartesian…

A:

Q: 1.23. Express the unit vector directed toward the point (x, Y, z) from an arbitrary point in the…

A: Express the unit vector directed toward the point (x, y, z) from an arbitrary point in the plane y =…

Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: Given information: The points are P(0, 0, 0), Q(5, 2, 2). Calculation: Find the vector valued…

Q: Find a so that the vectors v = i- aj and w = 7i + 7j are orthogonal. ..... une on integer or o…

A: If two vector orthogonal then dot products will be zero

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.