Consider the following lines: r(t) = (3t + 2, 2t +2, 4t + 4), R(t) = (s+ 1, 4s – 2,-5s + 9), -o 0 and s > 0 measure time in seconds.

Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: Find the equation of the plane that X-3 contains the lines =y= z+1 4 and X+2= =y-5= 2 Z-3 4 2 -16x -…

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Q: 6. Find the symmetric equation of the line parallel to ở = (1,4, 6) + t(−2, 4, 7) that intersects…

A: Given problem:- 6. Find the symmetric equation of the line parallel to r = (1,4,6) + t(−2, 4, 7)…

Q: Find a plane containing the point (7,-8,8) and the line F(t) = +t

A: Given that, the point is 7,-8,8 and the line is r→t=-6,-8,-7+t6,8,4. From the given line, the point…

Q: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

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Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: line through the variable point A(k+1,2k) meets the lines 7x+y-16=0 ,5x-y-8=0,x-5y+8=0 at…

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Q: Find an equation of the plane orthogonal to the line which passes through the point (-9, 10, -6).…

A: given equation of orthogonal line

Q: point P(1, 1, –3) and orthogonal to the plane 3y – 4x + 2z = 3. |

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Q: [1 |A = [a1, a2, a3, a4] 2 11 5 0 3 -1 4 0

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Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

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Q: A laser pointer is situated at the point (3, 1, 4) and is pointing a linear beam in the direction…

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Q: Find the condition for the points(a, 0).(h, k)(0, b) when ab 0 to be collinear.

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

Q: x(t) Find a plane containing the point (6,-4,4) and the line y(t) z(t) 3 + 3t -3+ t 6 + 3t

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