Question

Прямые (x-1)/4=(y-2)/m=(z-3)/4 и (x-3)/2=(y-4)/3=(z-5)/2 параллельны при m= ?

Answer 1

Координаты направляющего вектора первой прямой a=(4;m;4)
координаты направляющего вектора второй прямой b=(2;3;2)
условие коллинеарности векторов:  a=α b
в нашем случае α=4/2=2 и m=2×3=6

Answer 2

To determine the value of "m" that makes the two given lines parallel, we can compare the direction ratios of the lines.

Let's consider the direction ratios of the first line, given by: (a, b, c) = ((x - 1)/4, (y - 2)/m, (z - 3)/4)

And the direction ratios of the second line, given by: (d, e, f) = ((x - 3)/2, (y - 4)/3, (z - 5)/2)

For two lines to be parallel, their direction ratios should be proportional to each other. In other words, we can express the ratios of their direction ratios as equal fractions.

Comparing the x-direction ratios, we have: (a/d) = ((x - 1)/4)/((x - 3)/2) = (x - 1)/(2x - 6) = 1/2

Simplifying the above equation, we get: 2(x - 1) = (2x - 6) 2x - 2 = 2x - 6 -2 = -6

The above equation is not possible since -2 is not equal to -6. This implies that the lines cannot be parallel for any value of "m". Therefore, there is no specific value of "m" that makes the two given lines parallel.