Direction ratios of two lines are a, b, c and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the direction ratios of the first line be $l_1, m_1, n_1 = a, b, c$.Let the direction ratios of the second line be $l_2, m_2, n_2 = \frac{1}{b

Vedclass · Accepted Answer

Parallel

Vedclass · Answer

(B) Let the direction ratios of the first line be $l_1, m_1, n_1 = a, b, c$.Let the direction ratios of the second line be $l_2, m_2, n_2 = \frac{1}{bc}, \frac{1}{ca}, \frac{1}{ab}$.Two lines are parallel if their direction ratios are proportional,i.e.,$\frac{l_1}{l_2} = \frac{m_1}{m_2} = \frac{n_1}{n_2}$.Calculating the ratios:$\frac{a}{1/bc} = a 	imes bc = abc$$\frac{b}{1/ca} = b 	imes ca = abc$$\frac{c}{1/ab} = c 	imes ab = abc$Since $\frac{a}{1/bc} = \frac{b}{1/ca} = \frac{c}{1/ab} = abc$,the direction ratios are proportional.Therefore,the lines are parallel.

Direction ratios of two lines are $a, b, c$ and $\frac{1}{bc}, \frac{1}{ca}, \frac{1}{ab}$. The lines are

Similar Questions

Find the octants in which the points $(-3, 1, 2)$ and $(-3, 1, -2)$ lie.

If a line makes angles $\alpha, \beta, \gamma$ with the positive direction of $x, y$ and $z$-axis respectively,then $\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma$ is equal to:

If a line has the direction ratios $-18, 12, -4,$ then what are its direction cosines?

If the coordinates of $A$ and $B$ are $(1, 2, 3)$ and $(7, 8, 7)$,then the projections of the line segment $AB$ on the coordinate axes are:

If the direction cosines $l, m, n$ of two lines are connected by relations $l-5m+3n=0$ and $7l^2+5m^2-3n^2=0$,then the value of $l+m+n$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module