Project the vector b = (1,3,1)" onto the line through %3D a13D (-1,2, 2)Т, (2, 2, –1)", аz 3D az= a3D (2, –1,2)".

Q: Determine whether the vectors (4, 2, 3)T , (2, 3, 1)T , and (2,−5, 3)T are linearly dependent.

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Q: Find terminal point Q of vector PQ =    <9, −2, 1>   with the initial point at…

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Q: Construct the vector 0.8 b+1.4 a having initial point P.

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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 a vector equation with parameter t for the line through the points (–1, –7, –4) and (-9, 8, 2).

A: we know that vector equation of line which passes through pointsx1,y1,z1,x2,y2,z2 is given by…

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 component form of vector RS with the initial point R(3,-2) and terminal point S(3,3)

A: From the given problem:   Initial point R3,-2   Terminal point S3,3   So the component form of RS→:…

Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

A: RECALL: Orthogonal vector:  Let us consider to vectors a→ and b→ then , cross product of a→ and b→…

Q: Sketch the given vector with initial point (1, 6). u = (-7, -4)

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Q: Find the vector v whose initial and terminal points are given below. (5.4, 2.4), (0.4, –2.6)

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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: 2- Are the vectores [4,2,6] and [6, 3, 9] collinear? How do you know?

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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: 3. Give two nonparallel vectors that are both orthogonal to (0, 5, 0).

A: Given A = (0,5,0) Let other two vectors be of type B = (a,b,c) A.B = a.0+b.5+c.0 A.B = 5b For…

Q: Find the terminal point of a vector of magnitude 5 that is parallel to the vector 1, 2, 3 and whose…

A: We will first find direction of vector using the magnitude and values of initial point and parallel…

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

A: Query- Find a vector orthogonal to the plane through the points -1,0,0,0,-2,-2,2,3,4. Answer- Let…

Q: Find a vector in 3d space whose magnitude is 4 and whose components have the largest possible sum

A: Find a vector in 3D space whose magnitude is 4 and whose components have the largest possible sum.…

Q: Project the first vector orthogonally into the line spanned by the second vector. 2 3 -2

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Q: are the vectors u=(-4,2) and v=(-1,2) orthogonal, parallel, or neither?

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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: A vector whose initial point is at the origin is called a/an________ vector.

A: Consider the given: A vector whose initial point is at the origin is called a/an________ vector. A…

Q: Suppose the pathogen is currently at location (1, 1) in antigenic space. Using a vector projection,…

A: We have to determine the vector that specifies the velocity at which the pathogen is evolving…

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

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Q: The terminal point of the vector v = 3i +5j – 4k with initial point (2, –1, 4) is

A: Follow next step

Q: Express the vector v with initial point P and terminal point Q in component form. P(3, 3), Q(5, 5)

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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: . Suppose ū = and i = ;). Construct a pair of orthogonal vectors from these two vectors.

A: See below the answer

Q: Determine the head of the vector;whose tail is (−3, 2). Make a sketch.

A: Consider (x, y) as the head of the vector. Then  -25=xy--32-25=x+3y-2

Q: Find two linearly independent vectors perpendicular to the vector 4 -7

A: This question can be solved using the concept of linearly independent vectors.

Q: Sketch the given vector with initial point (7, 5). %3 (4, 2) u =

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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: The terminal point of the vector v = i +2j +3k with initial point (4, 2, –3) is

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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 a nonzero vector orthogonal to the plane through P(2,5, 1), Q(-3, 1, –2) and R(5, –3, –1).

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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: Determine the vectors axe linear yy independent -3 2. 8. O ON

A: For linearly dependent determinant  of matrix is zero D=0

Q: Construct the vector -a-2 b having initial point P.

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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: What helps to set of vectors linearly independent?

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Q: 2) Find the vector from the origin to the center of the sphere 2x² + 2y² + 2z2 + 4x - 4z = 0.

A: The equation of the sphere is, 2x² + 2y² + 2z² + 4x - 4z = 0 So, x² + y² + z² + 2x - 2z = 0 So, (x²…

Q: Find a nonzero vector orthogonal to the plane through P(2, 5, 1), Q(-3, 1, – 2) and R(5, –3, –1).

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Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

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Q: Show the process of Reflecting a vector/matrix about a line that goes through the origin?

A: Reflection of vector/matrix about a line that goes through the origin: When we reflex a point about…

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

A: This could be solve using vector concept.

Q: Is the line passing through the point (3/2, 1) and slope −2 a hyperplane ? If yes, identify this…

A: Any line in 2D is a hyperplane.  ax+by=c, is a hyperplane (a,b) is called the normal vector  c is…

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: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

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Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

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

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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…