Let L be the line through the point Q=(-6, 9, -11) and direction vector [-1,2,-2]. Find the two distinct points R1 and R2 on L at distance 3√10 to the point P=(-4,2,-1) R1 = (0, 0, 0) R2=(0, 0, 0)

Q: The distance from the origin to the line passing through the points (0, 1,3) and (1,-1,2) is 14.

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Q: Find x such that the line through (2, - 3) and (3, 2) is perpendicular to the line through (- 2, 4)…

A: We have the points A(2,-3),B(3,2),C(-2,4) and D(x,-1) We have to find the value of x such that the…

Q: Find an equation of the line through (-2, 5, 3) that is perpendicular to both u = (1, 1, 2) and the…

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Q: Find a set of symmetric equations for the line “A" perpendicular to the lines having direction…

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Q: Let Lz be the line passing through the point P-(10, 1. –10) with direction vector d--2, -2, 3]", and…

A: We will use formula for the shortest distance.

Q: Is the line through the points (3, 4) and (-1, 2) parallel to the line 2x + 3y = 0? Justify your…

A: Given two points: 3, 4 and -1, 2            ……1   Given line: 2x+3y=0                       ……2

Q: Find a direction vector for the line containing the points (-1, 5, 2) and the point (2, 3, - 1).

A: We have to find a direction vector for the line containing the points -1, 5, 2 and 2, 3, -1. We know…

Q: i 6i + 2j+ 2k + 2(i- 2j+2k) Find the shortest distance between lines -4i -i + 4(3i - 2)- 2k) and

A: The given lines are as follows- r→=6i^+2j^+λi^-2j^+2k^          ........(1)r→=-4i^-k^+μ3i^-2j^-2k^…

Q: Find equations for the followingineF - The line through y and parallel to Z-axis

A: To find the equation of the line that passes through 1, 1, 1 and parallel to the z‐axis.