u =  -1 2 v=  -3 3 display the following vectors on a xy-graph: u, v, -v, -2v, u+v, u-v. Is every vector in R^2 a linear combination of u and v?

Q: Consider the vectors [2, 1,0, 2|], [3, 1,0, 1), [1,1, 0, -1] in R. Decide whether they independent.…

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Q: If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not…

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Q: The vector v= (6,-4, 0) starts at the point P = (-2,5, -1). At what point does the vector end?…

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Q: Find the vector P,P2 and P2P1 P:(3.2,3) , Р.(5,7,-1) b- P1(-2,-1,0), P2(4,-5,2) a - P1(0,3,3),…

A: We can solve the given problem as follows:

Q: The intersection of the two planes given by the vector equations -2 = -1 and -2 r. -4 = 6 4 is

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Q: Graph the two vectors x= (5, 1,3) and y=(-1,3,1

A: Topic:- 3D

Q: Express the vector of the form v=vi+ v2j + v3k. AB if A is point (-9, -2, 1) and B is point (-4, -9,…

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Q: (a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors (1,…

A: We have to check

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Q: Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). 7(t) =…

A: The vector equation of a line passing through any two points with position vectors a  and  b is…

Q: Find a vector equation with parameter t for the line through the points (-1, –7, –4) and (-6, 8, 2).…

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Q: The line that passes through the point (4, –2, 0) and parallel to the vector (1, 2, –3) has…

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Q: :) Find symmetric equations for the line that passes through the point (2, –-5, 9) and is parallel…

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Q: Express the vector in the form v = V¡i + v2j + v3k. P2 if P1 is the point (4, -5, 6) and P2 is the…

A: Given :                      P1 4,-5,6 and P2 6,-8,2

Q: If the vectors ü =[-9, a, 15] and V= [b, 2, - 5] are collinear, then: a = 6 and b = -3 Oa = -6 and…

A: by using collinear concept

Q: Given the two points A(1,2,3) and B(2,-3,4) which of the following is the vector equation passing…

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Q: Give the parametric and symmetric equations of the line that passes through the point (2,6, –1) and…

A: To find equation of line passing through the point 2,6,−1 and perpendicular to both vectors −4,3,−5…

Q: Find the equation of the plane through the point (-3,2, 0) and perpendicular to the vector (1,-2,5).

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

Q: If possible, write the vector w as a linear combination of the vectors V₁, V2, ..., Vk. If it is not…

A: a) Given:     w=1,1,5, v1=7,7,7      v2=2,5,3, v3=4,1,-1 w=i^+j^+5k^, v1=7i^+7j^+7k^…

Q: A company manufactures two products. For $1.00 worth of product B, the company spends $.45 on…

A: We want to find cost per dollar of income.

Q: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find The equation of the line through (1,2,3) with…

A: Given vectors u=(1, -3, 5)  v=(2, 1,-3)  And line passing of point (1, 2,3)

Q: What is the component form of the vector represented by 8a when a = (-5, 3)? Enter the answer in the…

A: Scale product of the vector

Q: The line that passes through the point (4, -2,0) and parallel to the vector (1, 2, –3) has symmetric…

A: The solution is given in the next step.

Q: The equation of plane through (3,-1,7) and perpendicular to the vector n(4,2,-5) is 4x + 2y5z-25 =…

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Q: 3. Give the parametric and symmetric equations of the line that passes through he point (4, –3, 5)…

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Q: Find the vector v = PQ. Р- (2, 1,4) Q = (-8.25, -4.25, 8) v =

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Q: Express the vector (-1,5,-6) in R^3as a linear combination of (2,0,7),(2,4,5) and (2,-12,13).

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Q: Suppose (vector u)=(3,-4,-5) and Vector v=(2,-1,2)u+v=?u-v=?v-u=?3u=?(-1/4)v=?2u-3v=?I appreciate…

A: u=(3,-4,-5)v=(2,-1,2)

Q: The symmetric equations for the line passing through (-3,–4, -5) and parallel to the vector (1,7,–…

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Q: ppose u = (-2, –1) and v = (-3,–9) are two vectors that form the sides of a parallelogram. Then the…

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Q: 3. Find a vector equation of the line that... a) passes through (-3,5,-2) and (7,-3,1)

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Find the equation of the plane that passes through the point (−2, 8, 4) and contains vectors ⃗a…

A: The equation of plane passing through the point x0, y0, z0 and contins vector a→ amd b→ is n1(x -…

Q: 4 2. Decide whether the vectors (1, 2,0,-1], [2, 6, -3, -3], [3, 10, -6,-5] are linearly…

A: Given vectors are ,  [ 1,2,0,-1 ] ,  [ 2,6,-3,-3 ] ,  [ 3 ,10 ,-6 ,-5 ]  (.)  The given vectors are…

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

A: Given: Let us assume, b= (1,3,1)T  a1=(-1,2,2)T   a2=(2,2,-1)T   a3=(2,-1,2)T

Q: Are the vectors -1, 3z-2z and-2z - linearly independent? choose If the vectors are independent,…

A: The objective is to determine whether the vectors -1,-3x-2x2 and -2x-x2 are linearly independent or…

Q: The vector equation for the line passing through the points (-4, 1,0) and (4, 4,-3) is r(1)-

A: It is given that the line passes through the points (-4,1,0) and (4,4,-3). Consider that the vector…

Q: Use vectors to determine whether the points (3,4,-1), (-1,6,9) and (5,3,4) are collinear.

A: The points (3,4,-1), (-1,6,9) and (5,3,4)

Q: . Find the direction cosines of the vector joining the two points (4, 2, 2) and (7, 6, 14).

A: Given that: Two points are (4, 2, 2) and (7, 6, 14)

Q: Provide the parametric and symmetric equations of the line that passes through the point (4, -3, 5)…

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Q: A line passes through points A(-1,-5, 9) and B(8, 5, - 15). A vector equation for the line is 7=(-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: Find symmetric equations for the line that passes through the point (5, -2, 7) and is parallel to…

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Q: Write the component form of a vector v with initial point P(8.6, -2.5) and terminal point Q (6.7,…

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Q: Find the linear equation of the plane through the point(1,2,3) and contains the line represented by…

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Q: a. Write the vector (-17, –18, 28) as a linear combination of a1 = (-4, -1,5), a2 = (-2, –3, 1) and…

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Q: Write the vector (7, 4,-12) vectors (-2, 1, 2), (1, 1, –2) as a linear combination (if possible) as…

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Q: By finding the dot product for each pair of vectors determine if they are perpendicular: (1,2) and…

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Q: Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the same…

A: The general equation of line in vector form is    .Then note the result : Line passing through the…