(a) Find a vector equation and symmetric equations for the line through the point (0, 14, 10) and parallel to the line x = −1 +2t, y = 6-3t, z=3+9t.

Q: Given the point A(2,1,-3) and B(6,-1,-5) write the vector equation and the parametric equations of…

A: Once we get vector form of the equation we can easily write the parametric form of equation of line.

Q: Find two vectors v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

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Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Find the vector and parametric equations of the line through the points A = (2,4,7) and B =…

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Q: Give the vector equation of the line passing through P and Q

A: To find the equation of the line passing through P and Q.

Q: 3. (7-9) A vector has an initial point at (1, –1) and an endpoint at (8, 6). Write the vector in…

A: The given start and endpoints of vector are (1,-1) and (8,6) We know that the magnitude of a vector…

Q: rite the equation of the line passing through P with direction vector d in vector form and…

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Q: Determine whether the lines L1 and L2 given by the vector equations are parallel, perpendicular, or…

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Q: Describe all solutions of Ax = 0 in a vector form, where -4 -2 0 3 2 0 0 0 1 1 A = -1 -4

A: Here given matrix is

Q: Find the vector equation of the line that contains the points (-17, 10,2). r(t)= ( ) +t ( and

A: Answer :

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 the vector equation for the line of intersection of the planes 5x + 3y2z = -1 and 5x + 5z = -4…

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Q: By finding the extreme values of f, find the shortest distance between Lị and L2. Be sure to fully…

A: Given that L1: v=2,4,4+t4,1,5L2: v=1,−3,2+t−2,3,1 To find the shortest distance between L1 and L2.