The line which passes through the origin and intersect the two lines x-1/2 = y+3/4 = z-5/3 , x-4/2 = y+3/3 = z-14/4 , is

Correct Answer is : x1x/11x = y−3y/-3−3y = z5z/55z

Correct Answer is : x1x/11x = y−3y/-3−3y = z5z/55z

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VITEEE 2017 Paper

Section: Mathematics

Question : 102 of 125

Marks: +1, -0

\frac{x-1}{2}

\frac{y+3}{4}

\frac{z-5}{3}

\frac{x-4}{2}

\frac{y+3}{3}

\frac{z-14}{4}

, is

Solution:

Let the line be

\frac{x}{a}

\frac{y}{b}

\frac{z}{c}

... (i)

If line (i) intersects with the line

\frac{x-1}{2}

\frac{y+3}{4}

\frac{z-5}{3}

, then

\begin{vmatrix} a & b & c \\ 2 & 4 & 3 \\ 4 & -3 & 14 \end{vmatrix}

= 0

⇒ 9a - 7b - 10c = 0 ... (ii)

from (i) and (ii), we have

\frac{a}{1}

\frac{b}{-3}

\frac{x}{5}

∴ The line is

\frac{x}{1}

\frac{y}{-3}

\frac{z}{5}

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