If the line joining points (2, 1, 4) and (a - | vedclass

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

Question

(A) The direction ratios of the line joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ are $(x_2 - x_1, y_2 - y_1, z_2 - z_1)$.For the first line joinin

Vedclass · Accepted Answer

$18, \frac{2}{3}$

Vedclass · Answer

(A) The direction ratios of the line joining $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ are $(x_2 - x_1, y_2 - y_1, z_2 - z_1)$.For the first line joining $(2, 1, 4)$ and $(a - 1, 4, -1)$, the direction ratios are $(a - 1 - 2, 4 - 1, -1 - 4) = (a - 3, 3, -5)$.For the second line joining $(0, 2, b - 1)$ and $(5, 3, -2)$, the direction ratios are $(5 - 0, 3 - 2, -2 - (b - 1)) = (5, 1, -1 - b)$.Since the lines are parallel, their direction ratios must be proportional: $\frac{a - 3}{5} = \frac{3}{1} = \frac{-5}{-1 - b}$.From $\frac{a - 3}{5} = 3$, we get $a - 3 = 15$, so $a = 18$.From $\frac{3}{1} = \frac{-5}{-1 - b}$, we get $3(-1 - b) = -5$, which implies $-3 - 3b = -5$, so $-3b = -2$, and $b = \frac{2}{3}$.Thus, the values of $a$ and $b$ are $18$ and $\frac{2}{3}$ respectively.

If the line joining points $(2, 1, 4)$ and $(a - 1, 4, -1)$ is parallel to the line joining points $(0, 2, b - 1)$ and $(5, 3, -2)$, then the values of $a$ and $b$ are respectively:

Similar Questions

If the line joining the points $A(7, p, 2)$ and $B(q, -2, 5)$ is parallel to the line joining the points $C(2, -3, 5)$ and $D(-6, -15, 11)$,then the value of $p^2 + q^2$ is equal to

The square of the distance of the point $\left(\frac{15}{7}, \frac{32}{7}, 7\right)$ from the line $\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ in the direction of the vector $\hat{i}+4 \hat{j}+7 \hat{k}$ is :

$\triangle ABC$ is formed by $A(1, 8, 4)$,$B(0, -11, 4)$ and $C(2, -3, 1)$. If $D$ is the foot of the perpendicular from $A$ to $BC$,then the coordinates of $D$ are

$P, Q, R$ and $S$ are four points with the position vectors $3i-4j+5k, 0i+0j+4k, -4i+5j+1k$ and $-3i+4j+3k$,respectively. Then,the line $PQ$ meets the line $RS$ at the point

The lines $x = ay + b, z = cy + d$ and $x = a'y + b', z = c'y + d'$ are perpendicular to each other,if

Vedclass Test Series

Exam Paper Generator

Online Exam Module