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

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: Given a line 2a + y = 2 in the two-dimensional plane, • If a given point (a, 3) satisfies 2a + B >…

A:

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: 1. What is the vector and parametric forms of the equation of the line passing through points…

A: This question can be solved using the concept of vector and parametric equation of line passing…

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: Write down the position vectors of any two points on the line ˜ r · (3i − 4j) + 2 = 0 and hence find…

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Q: Find a vector normal to the plane with the given equation.9x − 4y − 11z = 2

A: Our Aim is to find a vector normal to the plane with the equation given below:-9x-4y-11x=2 -(i)

Q: Parametrize the line that passes through the point (1,2,3) parallel to the vector v = -3i + 7k.

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Q: Find an equation of the plane through the point (2,1,-3) with normal vector 2i-3j+k. Determine the…

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Q: Find an equation of the plane. the plane through the point (5, 6, 5) and with normal vector 6i + 8j…

A: As we know that the equation of the plane which is passing through a point Px0,y0,z0  and normal…

Q: A dog searching for a bone walks 3.50 m south, then runs8.20 m at an angle 30.0° north of east, and…

A: According to the given function draw the graph of the function:

Q: | Find a vector equation for the line through the point (–9, –9, 3) parallel to the line 19 + 4t, y…

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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 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: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

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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: Parametrize the line segment joining the points P(1, 2, 0) and Q(1, 3, -1).

A: We know that equation of line passing through the points (x1,y1,z1) and (x2,y2,z2) is

Q: Parametrize the line that passes through the point (1, 2, 3) parallel to the vector v =-3i + 7k.

A: WE know that equation of line through (x1,y1,z1) and parallel to vector ai+bj+ck is

Q: Find the parametric equations of the line through the point P(1, 2, 4) and parallel to the vector .

A: use the parametric form  of line .

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 the vector equation of the line that passes through point M(1, 1, 2), intersects the following…

A: Question is solved.

Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4

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Q: Find a vector in component form that is perpendicular to the line 3x 4y = 6.

A: To find the vector in component form that is perpendicular to the given line.

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

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Q: Find the parametric equation for the line through the point (2,-3,1) and parallel to the vector…

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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: 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: 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: What vector has the same magnitude as the vector u = (4,-3) and points in the opposite direction?

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Q: Determine the vector and parametric equations of the line through A(6,2,5) and B(9,2,8)

A: Given points , A(6,2,5) B(9,2,8) Therefore a=6i+2j+5k b=9i+2j+8k

Q: o v based at the origin.

A: Sketch the vector v = (2, −3) based at P = (1, 4) and the vector v0 equivalent to v based at the…

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 line through p = (3, 2, 2) in the direction of v = (-1, –4, 2) in vector parametric form:…

A: We have to write the line trough p=3,2,2 in the direction of v¯=-1,-4,2 in vector parametric form.

Q: Find the parametric equations of the line containing the point (-2,1,2) and parallel to the vector…

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Q: Find a vector parametrization of line through P = (9, 8, 3) in the direction v = (4, -8, 6). %3D…

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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: 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 vector parametric equation for the line through the point (−1,−1) that is perpendicular to…

A: Vector equation of line which passes through point r0 and perpendicular to line a+bt,c+dt is given…

Q: Give a vector parametric equation for the line through the point (4, 0, -5) that is parallel to the…

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

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Q: generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then…

A: We know that equation of line through (x1,y1,z1)  and parallel to ai+bj+ck is

Q: Parametrize the line that passes through the point (1, 2, 3) rallel to the vector V = -3i +7k .

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

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Q: Sketch the curve with the vector equation 7(t) = (t,2 – t, 2t). Indicate with an arrow the direction…

A: Solution

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.