A vector equation for the line 2 a+12 y- 8 z = 78 L: -6 a + 8 y+ 2 z = 8 is given by 4 r ER -1 -5 金 3 5 +r| 3 r ER -5 () -3 1. r eR 5. 4 +r| 2 r ER 1 -2 +r r ER None of the other options.

Q: 13. Find a vector equation of the line through (2, 1) parallel to (x, y) = (-2,7)+t(3,5). 14. Find a…

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Q: 3. What value of k will make the line with symmetric equations - (1,−1,3)+s(3,2,2) p vector equation…

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Q: Add the vectors u (0, 3) and i = (- 2, – 1) graphically. Your graph should include u, v and the…

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

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Q: Write down the equation of the line that passes through the points (5, -1, 2) and (3, 1, 1). Using…

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Q: Which of the follow is the direction vector of the line 7=(2, 1, 3) + t(-7, 1, 6) (7, 1, 6) O(-7, 1,…

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Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

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: What is the Direction vector for the line with Cartesian equation 3x + 2y-1= 0

A: Any line in two-dimensional Euclidean space can be described as the set of solutions to an equation…

Q: Suppose the solution set of a certain system of equations can be described as x1 = 5 – 4t, x2 = -6 –…

A: Given solution set is x_1=5-4t, x_2=-6-2t ,x_3=4t-5 ,x_4=3t-3 . Now we will use the vector notation…

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: The distance of a point in the 3-D system from the origin A. is defined by the absolute value of the…

A: Given :                To find the distance of a point in the 3-D system from the origin

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: 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: Find the vector equation of the line, L that passes through the points P (2, -2, 8) and Q (10, 8,…

A: Given query is to find the equation of the line passing through indicated points

Q: Find the vector in the same direction as <1, 1, 0> whose component in the direction of <2,…

A: Let  us suppose that

Q: The scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

A: The scalar equation of a line is of the form Ax+By+C=0

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: 2. Find a vector equation of the line through (1, 0, −3) and (2, 4, 8). Make sure to justify your…

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Q: What is a general equation for the line with vector equation x=[31]+t[4−5]

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Q: a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4]

A: To find the equation of line.

Q: Determine the vector equation of a line that is perpendicular to the line, p = |-4, 4, 9 + t|-1, 3,…

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Q: through the point (−2,4) and is perpendicular to the line  x=[31]+t[4−5] is

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Q: u = (- 4, -1,1) and v = (8, -4,3), a unit vector in the direction of the vector w = 3u-v corresponds…

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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: Which of the following is a direction vector for the line through А (3, — 2) and В (1, 2)? Select…

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Q: The position vector of a moving particle, at time t is given by 7= 2 127- -> 10 t j + 4 (t +2 k…

A: We use the definition of velocity and speed to find the velocity and speed of a particle at the…

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

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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: Find a direction vector for the line containing the points (-1, 5, 2) and the point (2, 3, - 1).

A: We have to find a direction vector for the line containing the points -1, 5, 2 and 2, 3, -1. We know…

Q: Q1) If a vector gets multiplied by a positive number, its direction * .will be reversed

A: Given statement : If the vector gets multiplied by a positive number, it's direction will be…

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: Express the vector v =-1 as a linear combination of the vectors -3 0,v2 4 and v3 -4 , if possible.…

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Q: Which of the following is the vector equation of a plane that contains the line x-3y+2 2-1 5 -23 and…

A: We know r→ = a→+s→+t→ From the equation of line, we get a→ = 3i^-2j^+k^ or we can write it as 3, -2,…

Q: 3. If a = 3x - 5y and b=-2x+9y, write the vector 5a-8b in terms of x and y

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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: Find symmetric equations for the line that passes through the point (5, -2, 7) and is parallel to…

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Q: Which of the following can be the vector equation of the line passing through the points (3,2,1) and…

A: We have to find the vector equation of the line passing through the points (3,2,1) and (5/2,1,-2).

Q: 1. For the cross product between vectors a=[h, -1, 8] and b=[k, 5, 7] to be axb= [-47, -5, 17], what…

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Q: Suppose the vector x characterizing the antigenic state of an influenza virus population changes…

A: The vector in the previous influenza season is 3/2, 1

Q: The equation of plane through (3,-1,7) and perpendicular to the vector (4,2,-5) is 4x + 2y5z-25 = 0.…

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Q: Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector 1.…

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Q: Find two vectors and īz whose sum is (-4, -2), where vy is parallel to (-2, -5) while ū, is…

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Q: Find the component form of the vector.

A: Consider the figure: Find the component of form of a vector v.   The component form of a vector in…

Q: Given that = <1, 2. 3) and - (4. 0. –4) find the vector where -W+37-0

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.