LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
212 views
in Geometry by (30.0k points)
closed by
Find the direction ratios of the line 2x = 3y = 5 - 4z ?
1. <2, 3, 5>
2. <6, 4, - 3>
3. <2, 3, - 4>
4. None of these

1 Answer

0 votes
by (53.7k points)
selected by
 
Best answer
Correct Answer - Option 2 : <6, 4, - 3>

CONCEPT:

The equation of a line with direction ratio <a, b, c> that passes through the point (x1, y1, z1) is given by the formula: \(\rm \frac{{x - {x_1}}}{a} = \frac{{y - {y_1}}}{b} = \frac{{z - {z_1}}}{c}\)

CALCULATION:

Given: Equation of line is 2x = 3y = 5 - 4z

Dividing the above equation by 12 we get

\(⇒ \frac{{2x}}{{12}} = \frac{{3y}}{{12}} = \frac{{5\ -\ 4z}}{{12}}\;\)

\(⇒ \frac{x}{6} = \frac{y}{4} = \frac{{z - \frac{5}{4}}}{{ - 3}}\;\)

By comparing the above equation with \(\rm \frac{{x - {x_1}}}{a} = \frac{{y - {y_1}}}{b} = \frac{{z - {z_1}}}{c}\) we get

⇒ a = 6, b = 4 and c = -3

So, the direction ratios of the given line is: <6, 4, - 3>

Hence, the correct option is 2.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...