Let P and Q be the points in R3 with position vectors p = (4, -6, 1) and q = (1, -3, -5), respectively. (a) Find the vector form of the equation of the line l through P and Q. (b) Determine the equation of the plane that passes through the origin and is perpendicular to l. (c) Determine the point where the line I intersects this plane.

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: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: 2. Given a line that passes through the point (-2,1,3) and is parallel to the line joining A(1,5,3)…

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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: 3) Find equations for the lines: The line through the point D/2 g. The line through (0,-7,0)…

A: Equation of line in 3D

Q: perpendicular to (x, y, z) = (1, -2,0) + r(1, -1, 1) through P(1, 3,5) [parametric equations]

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Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

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Q: 3) Find equations for the lines: a. The line through the point P(3,-4,-1) parallel to the vector…

A: Here we have to find the equations for the lines,  a) The line through the point P(3,-4,-1) and…

Q: 3. Given two points P(4,0,2) and Q(2,-1,3), find the equations of the vector PQ, the line passing…

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