Find symmetric equations of a line that contains the point (13,3,7) and the origin. Demonstrate how to check (13,3,7) and (0,0,0) that they fit the equation of the line.

Q: A straight line has vector equation given by r=(1-A)i+(3+2A)j.How far is this line from the origin?

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Q: Find the new equation of the line y=x after applying the translation by the vector (2, -1)

A: New line will be shifted to 2 units right and 1 unit down.   Point on x axis (2,0) Point on y axis…

Q: a line is parallel to the vector i+ 5j+3k and passes through the point P = (6, 2, 4), then the…

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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: (b) Find the points in which the required line in part (a) intersects the coordinate planes.

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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 the plane that contains:  P1(-1,1,-2), P2(-2,2,4),P3(0,2,-2)

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Q: plot the given pair on a cartesian plane {(1,1),(2,4),(3,7),(4,10),(5,13)}

A: The given pair of points are  A(1,1), B(2,4), C(3,7), D(4,10), E(5,13)

Q: Find the scalar equation for each line: (a) a line through the point (-6, 7) with direction vector…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3. Find an equation of the plane passing through the points (1, 2, -6), (2, 3, -2), and (-1, 4, 8).…

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Q: Let / denote the line in R with equation y = = 3x - 2. Let Q = (2, -1). (a) Write the line / in…

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Q: Find the scalar equation of the plane that contains the line x+1 -3=. and is parallel to x+2=+4_:+2…

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

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Q: Use the cross product to find an equation for the plane that passes thru the points (1, 2, 3), (4,…

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