Find the equation of the line passing through | vedclass

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Question

(A) Let the direction ratios of the required line be $(l, m, n)$.Since the line is perpendicular to the lines with direction ratios $(3, -16, 7)$ and

Vedclass · Accepted Answer

$\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z + 4}{6}$

Vedclass · Answer

(A) Let the direction ratios of the required line be $(l, m, n)$.Since the line is perpendicular to the lines with direction ratios $(3, -16, 7)$ and $(3, 8, -5)$,we have:$3l - 16m + 7n = 0$ and $3l + 8m - 5n = 0$.Using the cross product to find the ratios $(l : m : n)$:$l = (-16)(-5) - (7)(8) = 80 - 56 = 24$$m = (7)(3) - (3)(-5) = 21 + 15 = 36$$n = (3)(8) - (-16)(3) = 24 + 48 = 72$Dividing by $12$,we get the direction ratios as $(2, 3, 6)$.Since the line passes through $(1, 2, -4)$,the equation is $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z + 4}{6}$.

Find the equation of the line passing through the point $(1, 2, -4)$ and perpendicular to the two lines $\frac{x - 8}{3} = \frac{y + 19}{-16} = \frac{z - 10}{7}$ and $\frac{x - 15}{3} = \frac{y - 29}{8} = \frac{z - 5}{-5}$.

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