The point of intersection of the lines repres | vedclass

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

Question

(A) Let the point of intersection be $P$. The coordinates of any point on the first line are $(1+2\lambda, 2+3\lambda, -1+4\lambda)$ and on the second

Vedclass · Accepted Answer

$3 \hat{i}+5 \hat{j}+3 \hat{k}$

Vedclass · Answer

(A) Let the point of intersection be $P$. The coordinates of any point on the first line are $(1+2\lambda, 2+3\lambda, -1+4\lambda)$ and on the second line are $(-1+\mu, -3+2\mu, 7-\mu)$.Equating the coordinates,we get:$1+2\lambda = -1+\mu \implies 2\lambda - \mu = -2$ ... $(i)$$2+3\lambda = -3+2\mu \implies 3\lambda - 2\mu = -5$ ... $(ii)$$-1+4\lambda = 7-\mu \implies 4\lambda + \mu = 8$ ... $(iii)$Adding equations $(i)$ and $(iii)$:$(2\lambda - \mu) + (4\lambda + \mu) = -2 + 8$$6\lambda = 6 \implies \lambda = 1$Substituting $\lambda = 1$ in equation $(i)$:$2(1) - \mu = -2 \implies \mu = 4$Checking these values in equation $(ii)$:$3(1) - 2(4) = 3 - 8 = -5$,which is correct.Substituting $\lambda = 1$ in the first line equation:$r = (\hat{i}+2 \hat{j}-\hat{k}) + 1(2 \hat{i}+3 \hat{j}+4 \hat{k}) = 3 \hat{i}+5 \hat{j}+3 \hat{k}$.Thus,the point of intersection is $3 \hat{i}+5 \hat{j}+3 \hat{k}$.

The point of intersection of the lines represented by $r=(\hat{i}+2 \hat{j}-\hat{k})+\lambda(2 \hat{i}+3 \hat{j}+4 \hat{k})$ and $r=(-\hat{i}-3 \hat{j}+7 \hat{k})+\mu(\hat{i}+2 \hat{j}-\hat{k})$ is

Similar Questions

The angle between the lines $3x + 2y + z = 0 = x + y - 2z$ and $2x - y - z = 0 = 7x + 10y - 8z$ is

Direction ratios of the line represented by the equations $x = ay + b$ and $z = cy + d$ are:

If the lines $\frac{x - 1}{-3} = \frac{y - 2}{2k} = \frac{z - 3}{2}$ and $\frac{x - 1}{3k} = \frac{y - 5}{1} = \frac{z - 6}{-5}$ are perpendicular to each other,then $k = \dots$

If the points $A(-1, 3, 2)$,$B(-4, 2, -2)$,and $C(5, 5, \lambda)$ are collinear,then $\lambda = $

If lines $\frac{1-x}{3}=\frac{7y-14}{2p}=\frac{z-3}{2}$ and $\frac{7-7x}{3p}=\frac{y-5}{1}=\frac{6-z}{5}$ are mutually perpendicular to each other,then $p = $ . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module