For the line that contains the points P(-1, 2, 4) and P2(3, 4, 7), find a) a direction vector. b) an equation for the line.

Q: Show that the lines having the equations 4x – 3y + 12 = 0 and 8x – 6y + 15 = 0 are parallel.

A: According to question,Given equation of lines,4x - 3y +12 = 08x - 6y +15 =0

Q: What is the equation of a line that is perpendicular to the line y = - x-1 and passes through the…

A:

Q: r1(t) = (3, –6, 2) +t (-4, 2, –4) r2(t) = (-3, 3, – 10) + t (2, 1, 0) Find the point of…

A: Lines r1 and r2 can be rewritten as follows:

Q: Find the symmetric equation of line L, that passes through the points (1, 8, 9) and (5, 9, 0).…

A: 9

Q: Determine whether the lines h and I, intersect, are parallel, or are skew. 1: n= 4i+3j+ (i-j+6k) 12:…

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Q: Find the coordinates of the point where the lines with the following equations intersect: 1 29 3…

A: Given Data: To find the coordinates of the point , 9x-12y=-4-3x+12y=12

Q: Let A be the point with coordinates (-2, -1, -1) and let B be the point with coordinates (2, 0, 0).…

A:

Q: a) Find the equation of the line passing through the point (4, -2) and (2, 8)

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Q: Determine whether the lines (1,1,1)+ t(1,2,-1), and (3,2,1)+(-1,-5,3) are parallel, intersect, or…

A:

Q: 9) 6x + 8 y = -22 y =-5 10) -7x +2y = 18 6x+ 6y = 0 11) 7x+ 2y = -19 -x+ 2y = 21 12) 3x– 5y = 17 y…

A: See the details solution in below

Q: i. Write the equation below in standard form. 1 3x 5 2

A: ii. Write the equation below in standard form y2-3x=15. i. Write the equation of the line passing…

Q: Find the equation of a line perpendicular to: a the line x+ 3y = 0 and passing through point (-3, 2)…

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: 3) Find equations for the lines: a. The line through the point P(3,-4,-1) parallel to the vector…

A: Here we have to find the equations for the lines,  a) The line through the point P(3,-4,-1) and…

Q: Find the point of intersection of the two lines l1 : 7 Intersection point:

A: Introduction: The point of intersection is the intersection of two lines or curves. A point is the…

Q: Determine the value of A so that the line whose equation is Ax + y = 2 is perpendicular to the line…

A: We are given 2 lines: The first (l1) has the equation Ax+y=2 The second l2 passes through the points…