15. Determine the vector, parametric, and Cartesian equations of each of the following planes: a. passing through the points P(1, 2, 5) and Q(3, 1, 2) and parallel to the line with equation L:7 = 2 + (41 + 3) + (1 + 1)k, teR b. containing the point A(1, 1, 2) and perpendicular to the line joining the points B(2, 1, -6) and C(-2, 1, 5) c. passing through the points (4, 1, -1) and (5, -2, 4) and parallel to the c-axis d. passing through the points (1, 3, 5), (2, 6, 4), and (3, -3, 3) T

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 an equation for the plane through the point (0, –4, 5) which is perpendicular to the line…

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Q: The parametric vector v=(6-t)i+(9t+8)j represents a straight line. Find the equation of this line

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Q: 3. Consider the points K (-1,0,7) and M(1, -2,5), the vector MN = (1,4, -3) and the li symmetric…

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Q: 1. a. The points (3,-1,2) and (-1,3,-4) are the endpoints of a diameter of a sphere i. Determine the…

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Q: Find an equation of the plane through the points P(0, 1, 1), Q(1, 1,1), and R(1,1,0). Write the…

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Q: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

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Q: Find a general equation of the plane through the point (2,9, 6) and parallel to the plane x + 5y +…

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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: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

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