Express the vector (-1,5,-6) in R'as (2,0,7), (2,4,5) and (2,-12,13). linear combination of

Q: The vector that has the same direction as ⟨3,4,3⟩ but has length of 4 is

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Q: Find the plane equation through point (3, -1, 7) and perpendicular to normal vector n = (4, 2, 5)

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Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: Definition used -                       If we have to write a vector as a linear combination of…

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: A vector orthogonal to the plane through the points (-1,0, 0), (0, 0,-2), (2, 3, 4) is

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

A: Solved below

Q: Find the vector with length V17 and same direction as = (7,0, -6).

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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: What is the terminal point of the vector a = (2, 2) based at P = (2,4)?

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Q: Find the vector projection of (3, 3, 4) onto (–1, -2, 2).

A: Projection of u onto v is given by.

Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

Q: Find a vector that is orthogonal to (−1, 2, 2)

A: Find a vector that is orthogonal to (−1, 2, 2)

Q: Consider the vector v between (-5, 5, –3) and (1, 1, 1).

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Q: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

Q: What is the component form of the vector with an initial point of (-2,5) and a terminal point of…

A: Given that ,  The vector with  Initial Point = (-2 , 5) Terminal Point = (7 , -3).

Q: how can i learnd about vector in r2 and r3?

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Q: Express the unit vector directed toward the origin from an arbitrary point on the line described by…

A: solution : Given the point x=0, y=3 and z1.22unit vector is defined…

Q: Find a vector orthogonal to both (-3, 2,0) and to (0, 2, 1) of the form (1,

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Q: Show that the vectors (1, 1, 1), (1, 2, 3) and (3, 3, 4) are linearly independent?

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, -2), (2,3, 4) is

A: A vector orthogonal to the plane through the points (-1,0,0) , (0,-2,-2) , (2,3,4) is

Q: Find a vector in the same direction as (3, –2) with length 10.

A: The vector that has the same direction as 3,-2 has the coordinates proportional to the given vector.…

Q: The normal vector of 2x + By - 16.7z = -8 is: ○ [2, 뮤, -16.7, 8) ① [호, 꽃, 16.7, -8] ① [올, 꽃, -16.7]…

A: We have given equation of a plane  92x+133y-16.7z=-8 Comparing this with the equation  lx+my+nz=d We…

Q: Find two unit vectors orthogonal to both (3,2,1) and (–1,1,0).

A: The vectors 3,2,1 and -1,1,0

Q: Express à = (3, 1, –1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: 2 Determine the tail of the vector 4 whose head is (3, –2, 2).

A: To determine- The tail of the vector 24-1 whose head is 3-22.

Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩

A: I have appended the formula used in the solution part of the question

Q: 3. find the length of the vector with initial point P(-3,4,1) and terminal point Q(-5,2,2)

A: Solution :

Q: Express the vector v with initial point P and terminal po P(-9, -7), Q(-3, -3)

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Q: Find two unit vectors orthogonal to both (6, 9, 1) and (-1, 1, 0). (vector with the smaller…

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

A: A vector is given

Q: Find the unit vector along the line joining point (2, 4, 4) to point ( - 3 , 2, 2). A) -0.8703ax -…

A: We can solve this as follows:

Q: Find two vectors and 02 whose sum is (2, –4), where is parallel to (2, -4) while vz is perpendicular…

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Q: Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and…

A: The given problem is to find the vector equation of line that passes through the given two points.

Q: Find a vector u € R' such that, at the point (2, 1, -1), the function f(, v, 2) =-y + 2a2 + has its…

A: Given, f(x,y,z)=-y3+2x2+z2

Q: Find the magnitude of the projection of (- 1, 2) onto the vector (3, 5)

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Q: Find two vectors v1 and vz whose sum is (-4, –4, 5), where vj is parallel to (1, 1, –2) while v2 is…

A: we have to find the two vectors v1→ and v2→ whose sum is -4,-4,5 where v1→ is parallel to 1,1,-2…

Q: Find a unit vector perpendicular to both (3,-2,4) and (-1,2,-3).

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1, -2), (2, 3, 4) is

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Q: Is it possible to write the vector (-5,11,-7) as a linear combination of the vectors…

A: See the attachment

Q: Find two vectors ūj and īz whose sum is (-5, –3), where vj is parallel to (2, 5) while īz is…

A: To find - Find two vectors v1¯ and v2¯ whose sum is -5, -3, where v1¯ is parallel to 2, 5 while v2¯…

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: Find a vector orthogonal to both (-4,5, 0) and to (0, 5, 4) of the form (1,

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Q: Express the vector v with initial point P and terminal point Q in component form. P(-4, 6), Q(-9,…

A: Given that the initial point is P-4,6 and the terminal point is Q-9,-4. The objective is to find the…

Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: Find a vector equation for the line segment from (2, -1, 4) to (4, 6, 1)

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Q: find two unit vectors orthogonal to (-1,-1,5) and (-5,-,3,3)

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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

Q: Find an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

A: Given An equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

Q: Find the magnitude of the projection of (- 5, 6) onto the vector (– 1, 0)

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