example of a vector equation for a line in 3 dimensions which doesn’t intersect the plane at z = 0

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: 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: 10 Find the vector equation of a line whose symmetric equations are z-1 y+3 %3D 3. -4 Express your…

A: To find the vector equation of a linewhose symmetric equations are   x-12=y+33=z-1-4.

Q: Find the linear equation of the plane through the point (6,−2,5) and with normal vector j+2k.

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Q: ASAP: find the equation of the plane that is parallel to the vectors (3,0,1) and (0,2,1) passing…

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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: 2. Find the vector, parametric and cartesian equation of a plane that contains the points А(-1,0,…

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Q: Write the equation of the plane with normal vector n = 11j passing through the point (12, 9, 10) in…

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Q: Give a vector parametric equation for the line through the point (3,4,−2) that is parallel to the…

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(-4, 8, 0),…

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Q: Expreas the unit vector dirccted toward the point (0,0, A) from arbitrary point in the plane --2. an

A: In this question, we have to find the unit vector toward the given point from the given plane the…

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

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Q: (a) Find a vector parallel to the line of intersection of the planes 4x + 3y – 2z = -5 and -5x + y –…

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Q: Determine vector and parametric equations for the line in R that passes through the points A(1,0, 1,…

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Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

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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: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: Two vectors Px1,y1,z1 and Qx2,y2,z2 Line segment P to Q: 1) Parametric form is…

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: ion cannot exist for a plane. 4. Determine the vector, parametric, and symmetric equations of the…

A: In this question, we want to find the vector, parametric and symmetric equations of the line Passing…

Q: Write the equation of the plane with normal vector n = i - k passing through the point (5, 2, –8) in…

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Q: (1 point) Find a vector equation for the line segment connecting the points P = (-9, –8, –1) and Q =…

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Q: 8. Determine a vector equation for the plane with Cartesian equation: 2x -y + 3z-24 = 0

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

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Q: (1 point) The planes 4x + 4y- z= 10 and 5x + 4y-4z 9 are not parallel, so they must intersect along…

A: The  intersection of two planes is always a line .

Q: (b) Sketch enough vectors in the vector field to get a sense of its geometric structure. (You should…

A: Given first order system of equation: dudt=u-1dvdt=v-1 the objective is to sketch the enough vectors…

Q: 3. Find an equation of the plane passing through the points (1, 2, -6), (2, 3, -2), and (-1, 4, 8).…

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Q: 3) Find a vector equation and parametric equations for the line segment that joins (-2, 4, 0) to…

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Q: Determine the scalar, vector and parametric equations of the plane that passes through the points…

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Q: How does translation T along vector AB affect the points in the plane?

A: Some information in the question is missing.

Q: Write an equation of the plane with normal vector n (7,5, -4) passing through the point (1, −5, 1)…

A: Given; n=<7,-5,4> Point (1,-5,1).

Q: What is a curve’s binormal vector? Give an example.

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Q: Find the general form equation of the plane through the origin and perpendicular to the vector (4,…

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Q: Give a vector parametric equation for the line through the point (4,-3) that is perpendicular to the…

A: Give a vector parametric equation for the line through the point (4,-3) that is perpendicular to the…

Q: Write an equation of the plane with normal vector n (7,5, −4) passing through the point (1, −5, 1)…

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

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Q: 5. Verify that its possible for a line with direction vector J=(2,1,-2) to lie flat on a plane with…

A: The vector equation of a plane is given by the expression . Here, and are the vectors that lie on…

Q: Find parametric (or vector) and symmetric equations of the line which pass through the points P,…

A: P11, 4, 6 & P22, -1, 3. Vector equation of a line passing through two points with position…

Q: a) Find vector equation and paramedrie equahion for the line that passes through the point (5,1,3)…

A: The objective is to find the vector equation and parametric equations for the given problem

Q: 2. Which does not exist for a line in three-space? a) vector b) parametric c) symmetric d) scalar

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Q: A vector with magnitude 10 points in a direction 310 degrees counterclockwise from the positive x…

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Q: Represent the line segment from P(−2, −3, 8), Q(5, 1, −2) by a vector-valued function and by a set…

A: Represent the line segment from P(−2, −3, 8), Q(5, 1, −2) by a vector-valued function and by a set…

Q: A) find a vector parallel to the line of intersection of the planes -3x - 2y - 2z = -1 and -4x - 2y…

A: Equation of line of intersection

Q: Determine an equation (in variables x, y, z) for the plane through the point (8, 1, 4), and with…

A: GIVEN- EQUATION OF PLANE PASSING THROUGH THE POINT (8,1,4) AND WITH VECTOR (-2,6,-2) TO FIND-…

Q: Write an equation of the plane with normal vector n= (2,8, -4) passing through the point (3,-9,-5)…

A: Vector equation of plane is used.

Q: Find vector and parametric equations of the plane that contains the point P = (-3,1,0) and is…

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Q: (a) Find a vector parallel to the line of intersection of the -2. 3y - 4z planes -x + 3y + 4z = 0…

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Q: Find an equation of the plane that passes through the point P(-7,-2,5) and has the vector n = (-7,4,…

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Q: Write vector and parametric equations of the plane. a) parallel to the xz-plane and through the…

A: If there is a constant k, then x = k represents a plane parallel to the yz-plane, y = k is a plane…