Give the parametric and symmetric equations of the line that passes through the point (5,−1,3) and is perpendicular to both vectors ⟨2,6,−1⟩ and ⟨−4,3,−5⟩

Q: Give the parametric and symmetric equations of the line that passes through the point (4, -3,5) and…

A: Using the dot product equal to zero for perpendicular to the vectors.

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

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Q: Find an equation of the plane through the three points P = (0, 0, 4), Q = (-3, 4, 0), R = (-1, -2,…

A: The given problem is to find the equation of plane passing through the given 3 points P(0,0,4),…

Q: Write the parametric equations of the line through the point (1,2,3) parallel to the vector a =.…

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Q: Write a vector equation for the line segment from (-3, 0, 0) to (0, 4, 3).

A: To write a vector equation for the line segment from -3, 0, 0 to 0, 4, 3. To write a vector equation…

Q: a = 2 ,8 ,2 ,−2 ,−4 ,−3 ,−11, −4 ,9 ,7 and b = 8,−1 . SOLVE Ax =b for x , and write x in…

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Q: Sketch the vectors = (2, 3,-6) and w = (-1,1,1) and draw -U, v + w and 7 - w.

A: The given vectors are

Q: Determine the parametric and symmetric equations for the line through the given points (2, –7,5),…

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Q: Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector…

A: The equation of a line that passes through the point: x0, y0, z0 is L=x0, y0, z0+ta, b, c, where a,…