Find a vector equation and a parametric equation for the line that passes through the point (5, 1, 3) and is parallel to the vector i + 4j – 2k.

Q: Find the vector parametric equations for the line. in the direction of the vector – i+ 5j-3 k and…

A: equation of line in vector parametric form

Q: Find the vector form of the equation of the line inR3 that passes through P = ( -1, 0, 3) and is…

A: Equation of a line passes through  x1, y1, z1 having direction ratios a, b, c is, x-x1a=y-y1b=z-z1c

Q: Find a vector equation for the plane that contains the points P, Q and R Find a scalar equation for…

A: Given points: P(2,1,1),Q(0,4,1),R(−2,1,4) and S(1,5,−4) Equation of a plane in cartesian form…

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

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Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, –6) + t(1,…

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Q: What is the vector parametric equation L(t) for the line through the points (5,-5,0) and (0,-3,3)?

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Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

A: Given that : P = ( 1, 0 ) and d = -13 .

Q: Find a vector equation with parameter t for the line through the point (7,0, –7) and parallel to the…

A: We have to find a vector equation with parameter t.

Q: Find parametric equations for the lines in The line through the origin parallel to the vector 2j + k

A: Given  The vector equation is  0i +2j+k  The line passing through origin , origin is  ( 0 ,0 ,0)…

Q: Ps Fnd Parametric equations for the 3. lines through (2,3,0) Perpendliculerr to the Vector uiitzj+3k…

A: First take cross product ie normal vector And then use formula

Q: Find parametric equations for the line through the origin parallel to the vector 3j + 9k. Let z =…

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Q: O Find the parametric equation of the line through the point (-3,1,6) parallel to the vector V 2i +…

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Q: Determine the vector equation of the plane 5x – 2y + 3z + 24 = 0. Verify mathematically that your…

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Q: 1 - Find a vector equation and parametric equations for the line segment connecting P(a, b, c) and…

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Q: Find parametric equations for the line whose vector equation is given. (а) (т, у) 3 (6, —5) + t(1,…

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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 equation of Plane that an contains the vector: and 1-6 and Z=36

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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: Determine the vector, parametric, and Cartesian (Scalar) equations for the line that passes through…

A: To find the equation of line that passes through the point A(4,-1) and is also perpendicular to line…

Q: Give a vector parametric equation for the line that passes through the point (–2, 1, –2), parallel…

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Q: 22. Given the symmetric equations t = - and t = +', find the vector equation of the line.

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Q: Find the vector and parametric equations for the line through the point P(-2, 1, -5) and the point…

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Q: find the component form of the vector. The unit vector obtained by rotating the vector {0, 1}120°…

A: To determine the unit vector.

Q: Find the vector parametric equations for the line. in the direction of the vector 57-5-k and through…

A:

Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

A:

Q: Determine the vector, parametric and cartesian (scalar) equations for the line that passes through…

A: First, we will find the cartesian equation of the line L through the points M(-2,0) and N(3,-3).…

Q: Find the vector and parametric equations for the line through the point P(-2, 4, -3) and parallel to…

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Q: Find:   a) the parametric equation of the line determined by points A(1,0,2) and B(2.2.1). b) the…

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Q: Find the vector parametric equations for the line. in the direction of the vector 4 i – 3j- 3k and…

A: Equation of the line passing through a given point a,b,c and in a given direction l i+m j+n k is…

Q: Write the parametric equations for the given vector equation: [2 [x, y, z] = [11,2,0] + t[3,0,0]

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Q: Find a parametric form for the line through the point (0, –7, -9) and parallel to the vector 6i – 7j…

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Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (2, –5) + t(1,…

A: Parametric equation of the line, <x,y,z>=<a,b,c>+t<p,q,r> , t is a scalar is given…

Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

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Q: find the component form of the vector. The unit vector obtained by rotating the vector {1, 0}135°…

A: The unit vector obtained by rotating the vector {1, 0}135° counterclockwise about the origin.

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

A:

Q: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

A: Given the point P=(-4,4) and the direction vector d=11We need to find the equation of line passing…

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 parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2+3t…

A:

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

A:

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 parametric equations for the line whose vector equation is (a) (x, y) = (3, –5) + t(1, –2) X =…

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Q: Rewrite the vector equation r(t) = (2+t)i + (1+3t)j + (-1+5t)k as the corresponding parametric…

A: We have to find the equation

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

A: Find a  vector equation and parametric equation for the line joining P and QP (1,-1,5) and Q (5,2,1)

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 parametric equations for the line whose vector equation is given. (а) («, у) %3D (3, —3) + t(1,…

A:

Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, –3) +t(1,…

A:

Q: Find a vector equation and parametric equations in t for the line through the point and parallel to…

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Q: find the component form of the vector. The vector from the point A = (2, 3) to the origin.

A: Find the component form of the vector. The vector from the point A = (2, 3) to the origin.

Q: write the equation of the plane passingthrough P with direction vectors u and v in (a) vector form…

A: P=(0,0,0) , u=212 and v=-321we have to find the equation of the plane passing through P with…

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.