If A(1, 2, 1),B(2, 3, 2),C(2, 1, 3),and D(3, | vedclass

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

Question

(A) First,find the direction vectors of lines $AB$ and $CD$. The vector $\vec{AB} = (2-1, 3-2, 2-1) = (1, 1, 1)$. The vector $\vec{CD} = (3-2, 2-1, 4-

Vedclass · Accepted Answer

$\overleftrightarrow{AB} \parallel \overleftrightarrow{CD}$

Vedclass · Answer

(A) First,find the direction vectors of lines $AB$ and $CD$. The vector $\vec{AB} = (2-1, 3-2, 2-1) = (1, 1, 1)$. The vector $\vec{CD} = (3-2, 2-1, 4-3) = (1, 1, 1)$. Since the direction vectors are identical,the lines are parallel. Now,check if the lines are the same by verifying if point $C(2, 1, 3)$ lies on line $AB$. The equation of line $AB$ is $\vec{r} = (1, 2, 1) + t(1, 1, 1) = (1+t, 2+t, 1+t)$. For $C$ to be on $AB$,$(1+t, 2+t, 1+t) = (2, 1, 3)$. This gives $1+t=2 \implies t=1$,$2+t=1 \implies t=-1$,and $1+t=3 \implies t=2$. Since $t$ is not consistent,$C$ does not lie on $AB$. Thus,the lines are parallel but distinct. Therefore,$\overleftrightarrow{AB} \parallel \overleftrightarrow{CD}$.

If $A(1, 2, 1)$,$B(2, 3, 2)$,$C(2, 1, 3)$,and $D(3, 2, 4)$,then which of the following is true?

Similar Questions

Show that the line passing through the points $(4,7,8)$ and $(2,3,4)$ is parallel to the line passing through the points $(-1,-2,1)$ and $(1,2,5)$.

The shortest distance between the lines $\frac{x-4}{1} = \frac{y-3}{2} = \frac{z-2}{-3}$ and $\frac{x+2}{2} = \frac{y-6}{4} = \frac{z-5}{-5}$ is:

The angle between the lines $\frac{x-1}{l}=\frac{y+1}{m}=\frac{z}{n}$ and $\frac{x+1}{m}=\frac{y-3}{n}=\frac{z-1}{l}$,where $l > m > n$ and $l, m, n$ are roots of the equation $x^3+x^2-4x-4=0$,is

The shortest distance between the line passing through the point $\bar{i} + 2\bar{j} + 3\bar{k}$ and parallel to the vector $2\bar{i} + 3\bar{j} + 4\bar{k}$ and the line passing through the point $2\bar{i} + 4\bar{j} + 5\bar{k}$ and parallel to the vector $3\bar{i} + 4\bar{j} + 5\bar{k}$ is:

$A(1, -2, 1)$ and $B(2, -1, 2)$ are the end points of a line segment. If $D(\alpha, \beta, \gamma)$ is the foot of the perpendicular drawn from $C(1, 2, 3)$ to $AB$,then $\alpha^2 + \beta^2 + \gamma^2 =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module