Find the stundand matices * and a for ToT,OT and て:→ド,1)- (-3y, fn + 3) T:→ド, 1.(4)): (J,)

Q: Find inner product of u, v and || u || if u = (1,2,5) and v = (2, –3,5). (Ctrl) -

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Q: 2)Passes point (1,3,7) and orthogonal to xy- plane.

A: The line which is orthogonal to x-y plane is lies on z-axis. Therefore the direction ratio's of the…

Q: How many paths are there from the point (0, 0) to the point (4, 5) in the plane such that each step…

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Q: Find the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

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Q: How many Potenhally defferent tensors of ander two can be defined by faking the ouer Product of sö…

A: The outer product of two tensors results a tensor with the order that equals the sum of the co…

Q: ɔ determine if the points (1, 3, 3), (3, -1, 5), (5, 2, 0), and (3, 3, 4) ie in tne same plane.

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Q: Find b and c so that  (9, b, c)  is orthogonal to both  (1, 2, 7)  and  (1, −2, 1).

A: To find b and c so that (9, b, c) is orthogonal to both (1, 2, 7) and (1, −2, 1).

Q: The line through the point (0, 1, 1) that is orthogonal to both ⟨0, -1, 3⟩ and ⟨2, -1, 2⟩.

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Q: 2) through: (-1, 5), parallel to y=-9x – 5 4) through: (-3, 4), parallel to y=-- 4 +3 3

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Q: Find mZU. U /3 V m2U = %3D Submit

A: tan x = perpendicular / base

Q: Determine the set of points satisfying the condition described by Iz – 2i| + |z + 4i| express in the…

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Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, - 1, 2) is parallel | to the line x=…

A: Given that points are (2,1,-1), (0,-2,0) and (1,-1,2) The parametric equation is,…

Q: What is the area of the parallelogram formed by the two vectors = (1,5) and = (-3,-2)?

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Q: Find a non zero unit vecor î that is orthogonal to u1= (1,2,1) and Uz= (2,5,4) in R³.

A: The given vectors are u1=(1,2,1) and u2=(2,5,4) in R3

Q: what is the parametric and symmetric eqvotions of the line that passes thrs point (4.-3,57 to beth…

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Q: as the sum of two orthogonal orthogonal to ư

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Q: Find projection of vector (0, 1, 0) into the line spanned by (0, 1,0) 0(-1,0, 2) 0(-1,3, 2) O (0, 3,…

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Q: Is the set of (infinite number of) vectors { (0,0,c) }, where c is a real number, a vector space…

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Q: Find projection of vector (0,1,0) into the line spanned by (0,1,0)

A: We have to find the projection of the vector (0,1,0) into the line spanned by (0,1,0).

Q: Find a plane containing the point (- 5, – 5, 2) and the line r (t) = (1, – 2, 1) + t(4, 7, 5).

A: Given that the required plane passes through the point P=(-5,-5,2) and required plane contains the…

Q: TheverticesofquadrilateralPQRSareP(-3,-1),Q(3,5),R(9,-1),andS(3,-7). a)ProvethatPQRSisarhombus.…

A: WE ARE GIVEN : quadrilateral PQRS are P(-3,-1), Q(3,5), R(9,-1), and S(3,-7). WE ARE TO PROVE: PQRS…

Q: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is the…

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Q: int at which the line ⟨4,−1,−5⟩+t⟨−3,3,2⟩⟨4,−1,−5⟩+t⟨−3,3,2⟩ intersects the plane…

A: Given the line 4,-1,-5+t-3,3,2  intersects the plane -x+y+z=18.

Q: Find mZB. 141° 72° B 47° mZB %3D Submit

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Q: Find a non zero unit vecor û that is orthogonal to u1= (1,2,1) and Uz= (2,5,4) in R³.

A: Cross product of two vector is perpendicular to both vectors.

Q: Find the eu. f line through the Pont (-2,3,4) and Parallel to e Planes: 2x +3y +42-5, 3X+4y+52 - 6…

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Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y- 2z=3 is: *

A: Plan 1: 4x-y+z=2 Plan 2: 2x+y+2z=3

Q: Let L, be the line passing through the point P-(1, -7, 5) with direction vector d-[1,-2, 0], and let…

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Q: What are the projections of the point (6, –3, 5) on the coordinate planes? On the xy-plane: ( On the…

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Q: Determine whether Hhe Lindependent. by inspection Vectors are linearly 6. -2 -3

A: A vector is given

Q: Find Vrand Viif Vi+2Vz=31-kand 3Vi-Vz sititk-

A: Given v1+2v2 = 3i-k  .........(1) 3v1-v2 = i+j+k  ......(2)

Q: what solid is formed when a right triangle is rotated around a line containing one of its legs

A: When a right triangle is rotated around a line containing one of its legs, a cone is formed .

Q: Detrmine Duf(4,-1,6) for f(x,y,z) = e^x2y  +  4zx3   in direction of (-3,2,6).

A: The given function is f = ex2y + 4zx3 To find directional derivative at (4, - 1, 6) in the direction…

Q: Prove that llu + vll2 + llu - vll2 = 2llull2 + 2llvll2 for all vectors u and v in Rn

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Q: Determine the number of (staircase) paths in the xy-plane from (1,2) to (5,4), such that each path…

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Q: Find the particular number of orthogonal transectories of x2+cy2=1 passing through the point (2,1)

A: Given equation is x2+cy2=1........1. We have to find the particular number of orthogonal…

Q: solve for orthogonal path

A: Given an equation y=c lnx Differentiating the given equation with respect to x, y'=cx  Therefore,…

Q: With the help of vector operation, find the area of the triangle that is deter- mined by the points,…

A: The points are (1,2,-1), (-1,0,2) and (4,-1,3)

Q: Find the vector v in the plane represented by the directed line segment from (4,-3) to (-2,6)

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Q: Sketch planeglven by Iz-31 = 1Z + lomplen the Cunve in the |ス-3| - |N+3i| 2. 2. 2. =フナ

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Q: Find a non zero unit vecor ô that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: We have to find a non-zero vector V that is orthogonal to u1=1,2,1 and u2=2,5,4 in R3.

Q: The plane through the points (2, 1, - 1), (0, -2, 0), and (1, -1, 2) is parallel to the line x 1-t,…

A: equation of plane for non collinear points , x-x1y-y1z-z1x2-x1y2-y1z2-z1x3-x1y3-y1z3-z1 we will use…

Q: Suppose v is a nonzero position vector in xyz-space. How many position vectors with length 2 in…

A: Given that, v is a nonzero position vector in xyz-space.

Q: What is the 270 degree clockwise rule which transformed the pre-image ordered pairs (5,-8) to it's…

A: Solution  Given image is transformed 270⁰ clockwise Pre image coordinates (x,y)=(5 ,-8) Image…

Q: Find a plane containing the point (-7,-3,-2) and the line of intersection of the planes 3x – 2y – 3z…

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Q: Find two vectors V1 and V2 whose sum is ⟨2,−5,3⟩, where V1 is parallel to ⟨4,4,0⟩ while V2 is…

A: Parallel vector will be multiple of each other  Perpendicular vector has dot products zero

Q: The distance from the point S(-7, 8, -4) to the plane 10x+2y+11z=2. 20 3 8 15 8 225

A: The equation of the plane is  10x+2y+11z = 2 The point is S-7,8,-4 To evaluate : The distance from…

Q: The plane containing the three points (2, –1, –1), (2, 1, 8) and (1, 0, 6). Please write th

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Q: Find the unit vectoru in the di rection of the vectorv=3(2, 2, 1).

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