A plane contains the point A(-1,2,5) and has direction vectors (2,-1,3) and (-3,1,5). Which of the following is a vector equation for the plane? a) (x,y,z) = (2,-1,3) + s(-1,2,5) + t(-3,1,5) b) (x,y,z) = (-3,1,5) + s(-1,2,5) + t(2,-1,3) c) (x,y,z) = (-1,2,5) + s(2,-1,3) + t(-3,1,5) d) (x,y,z) = (-1,2,5) + s(2,-1,3) + t(-8,-19,-1)

Q: be the line through the point with coordinates (0,1,0) in the direction of the vector h of the…

A:

Q: he points A(1,-2,4) and B(2,-4,1) cach make direction vectors with the point (Xo.Yo, Zo). The point…

A: The Parametric equations of the line are the components of the vector equation , and have the form…

Q: Determine (x, y, z) for each figure. Then find the component form of the vector from the point on…

A:

Q: Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a rectangular…

A: Question- Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a…

Q: Q1) Find the equation of the plane passing through the point (4,-1,-5) and perpendicular to the…

A: We have to find the equation of the plane passing through the point (4,-1,-5) and perpendicular to…

Q: Which of the following vectors is/not perpendicular to the line whose direction vector is (2,-3,5)?…

A:

Q: Which vector equation below represents the line in R³ that passes through the point (-4, 5, 7) and…

A:

Q: 2. Find the equation of the planes: a) (in general form) that goes through the three points A(4, 0,…

A:

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

A:

Q: Construct a vector that is perpendicular to the plane containing (−2, 4, 1),(3, 3, -1) and (1, 0,…

A: Construct a vector that is perpendicular to the plane containing (-2,4,1),(3,3,-1) and (1,0,2)

Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

Q: Line E goes through the points (1, 5, 2) and has the direction vector ⟨2, 2, 3⟩. Line F goes through…

A:

Q: 3. A plane contains A(1, -3, 2), B(-2, 4, 2) and C(3, 2, 1). (a) Determine the vector equation of…

A:

Q: Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A:

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

A: Given:equation of two planes To find:vector equation of line that intersects these planes

Q: Find an equation of the plane that is parallel to the vectors and , passing through the point (3,…

A: Use given parallel vectors <1,-3,1> , <4,2,0> and passing through the point (3,0,-2)…

Q: Given the points A(3,-1,1), B(2,3,4) and C(4,1,1). (a) Find a unit vector that is simultanously…

A: Concept: A plane going through three non-collinear points has the following equation: Vectors and…

Q: Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and…

A: The given problem is to find the vector equation of line that passes through the given two points.