Find a vector equation and parametric equations in t for the line through the point and parallel to the given vector. (Po corresponds tot = 0.) Ро - (4, -6, 3) (1.2.-3) i+ j + k r = X = y = z =

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: Find both the vector equation and the parametric equations of the line through (0,0,4) in the…

A: Explanation of the answer is as follows

Q: Find a vector equation for the line through the point (-6, 4, 1) perpendicular to the vectors u =…

A: A line passes through the point -6,4,1 and perpendicular to the vectors u→=-1,-2,3 and v→=3,-8,-9 We…

Q: Find parametric equations for the line whose vector equation is given (a) (x, y) = (3, –5) + t(1,…

A: A)x, y =3, -5 + t 1, -2x, y =3, -5 + t, -2tx, y =3+t, -5-2t Parametric equations of the line:x= 3 +…

Q: 1. Determine the vector and parametric equations of the line passing through P(-2, 3, 5) and Q(−2,…

A: According to our guidelines we can only solve the first question and rest of the questions can be…

Q: Determine a vector equation for the line that is perpendicular to 7 = (4, 1) + s(−3, 2), sER, and…

A: We need to find the equation of line perpendicular to r→=(4, 1)+s(-3, 2),  s∈ℝ and passing through…

Q: 1.Find the vector equation and parametric equations of the line passing through the point P(5, 6, 7)…

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Q: Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0…

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Q: Given the points A(2,6,0) and B(3,5,6) determine the equation of a line vector in parametrix form

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Q: Find a vector equation for the line segment from (2, -4, 6) to (5, 5, 5). (Use the parameter t.)…

A: a→=2i-4j+6kb→=5i+5j+5kn→=b→-a→=3i+9j-k

Q: Find the vector equation of the line that passes through (1,0,-3) and it's parallel to v=2i - 4j +…

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Q: Let L be the line with parametric equations x = −3+2t y = 8+t z = 5+3t Find the vector equation for…

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Q: Find both the vector equation and the parametric equations of the line through (4,3,6) that is…

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Q: Given a point M = (5,–3,–2) on a line in space and a parallel vector to the line defined as vector d…

A: Parametric equations of a line  in 3-D space are given byx = x0 + t a , y = y0 + t b , z = z0 + t c…

Q: 13. Find an equation of the plane through the point (1,2,3) and perpendicular to the vector…

A: Given a point P( x, y, z) and a vector (a, b, c) which is perpendicular to the given plane

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

Q: The Cartesian equation of the straight line tangent to the plane curve given parametrically by the…

A: This question can be solved using the concept of tangent and normal under application of…

Q: 1. Give the vector equation of a line perpendicular to the line L: x= 21-1, y=-31, 1 e R. Are there…

A: Given line: l:x=2t-1, y=-3t, t∈ℝ To find the other line The vector equation of the line is…

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A: Use the direct formula for equation of plane passes through a point and with given normal vector.

Q: Find a vector equation for the line segment from (2, -4, 5) to (6, 4, 4). (Use the parameter t.)…

A: Explanation of the solution is given below...

Q: Find a vector equation for the line segment connecting the points P = (-9,–6, 8) and Q = (-15,…

A: We have to find a vector equation for the line segment connecting the points P=-9,-6,8 and…

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) and (5,2,4),…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Here we find the vector and parametric equations of line.

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

A: Given problem:- Find the vector equation of the line, L that passes through the points P (2, -2, 8)…

Q: Give a vector parametric equation for the line through the point (4, 2) that is perpendicular to the…

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Q: In vector form, the equation of a line is given by r = (0, 1, 2) + t(2, 1,0), where t e R. T…

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Q: 3. Find the equation of the line that goes through the point (1, 3, 2) and is parallel to the line…

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

Q: Find a vector equation and a parametric equation for the line that passes through the point (5, 1,…

A: We have to solve given problem:

Q: Find a vector equation for the line through the point (2, 5, 8) perpendicular to the plane 2x + 5y +…

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Q: Subtracting the two equations, find a vector equation for the curve of 3 intersection between y =…

A: Here, the two equations are y=4x2+34z2  and  y-1=3x2+12z2 for x>0. We will be finding a vector…

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: Find the linear equation of the plane through the point (-3, 4, 3) and perpendicular to the line…

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Q: 5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6…

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, −1,…

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

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Q: Give a vector parametric equation for the line through the point (-1, –1) that is perpendicular to…

A: We have to write a parametric equation of the line  which is passing through the point (-1, -1)…

Q: a. Find vectors nį and n2 that are normals to II and IL respectively and explain how you can tell…

A: The planes are given by π1: x1x2x3=0-33+λ11-12+λ2313 and π2: x1x2x3=000+μ112-1+μ2340. For π1:…

Q: snip1

A: The given point is, P=1,2,-1 which is parallel to the vector d=5-13. The objective is to find the…

Q: Give a set of parametric equations for the line L4 that lies tangent to the graph of the vector…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: u = < 0,2,2>  w = < 2,-2,0>  U× W is perpendicular to both u and w

Q: Give a vector parametric equation for the line through the point (1,−4,1) that is parallel to the…

A: We have to find the vector parametric equation for the line through the point (1,-4,1) that is…

Q: Find a vector equation and parametric equations for the line segment that joins P to Q, given P(0,…

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Q: Find a vector equation for the line that goes through the points (5,9,0) and (0, 11, 1). F(1) = with…

A: A ( 5,9,0) B ( 0,11,1)

Q: Find the distance of the point (2, 6, –4) from the line r(t) = (-1 + 31, –1+41, 5 – 2t). Give a…

A: Consider the given point as, 2,6,-4  And the line -1+3t,-1+4t,5-2t

Q: 2. Find a vector that has the same direction as (-3, 5, v2), but has length 8. 3. If ā = 21 – 43+ 4k…

A: We'll answer one question since the exact one wasn't specified. Please submit a new question…

Q: Find the vector equation of the line passing through the point (1, 2, - 4) and x-8 y+19 z-10 x-15 у…

A: To find the equation of line perpendicular to the given lines first we find vector perpendicular to…

Q: Subtracting the two equations, find a vector equation for the curve of intersection between y=…

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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.