Geometry

3D Coordinate Geometry

3D Coordinate Geometry - Equation of a Line

         

If the line represented by x−22=y−33=z−125\frac{x-2}{2} = \frac{y-3}{3} = \frac{z-12}{5} passes through the point (4,(4, a,a, b)b), what is the value of a+ba+b?

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by Brilliant Staff

A line l l is parallel to the planes −4x+y=0 -4x + y = 0 and x+5z=0. x + 5z = 0. Given that it passes through the point (4,0,6), (4, 0, 6), find the equation of l l in the simplest form of x−ap=y−bq=z−cr. \frac{x-a}{p} = \frac{y-b}{q} = \frac{z-c}{r}.

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The following are the equations of lines that are parallel to one another: {x−12=y−2p=z−4p,x−2q=y−42=z−73q−q2,x50=y11r−10=zr2. \begin{cases} \frac{x-1}{2} = \frac{y-2}{p} = \frac{z-4}{p} _, \\\\ \frac{x-2}{q} = \frac{y-4}{2} = \frac{z-7}{3q-q^2}_, \\\\ \frac{x}{50} = \frac{y}{11 r - 10}=\frac{z}{r^2} _. \end{cases} Find the value of p+q+r.p+q+r.

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The following is the equation of a line with direction vector d⃗=(p, q, 10):\vec{d} =(p,\text{ }q,\text{ }10): 2x−u4=y−22=z−25.\frac{2x-u}{4}=\frac{y-2}{2} =\frac{z-2}{5}. If the line passes through the point (4, 4, 7),(4,\text{ } 4,\text{ } 7), what is p+q+up+q+u?

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If the two lines x−42=y+33=z−44 and x−6=y−k2=z−3 \frac{x-4}{2} = \frac{y+3}{3} = \frac{z-4}{4} \text{ and } x-6 = \frac{y-k}{2} =z-3 intersect, what is k?k?

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