If the distance of point B(2, 1, -3) from the | vedclass

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

Question

(D) The line passes through $A(4, -2, 2)$ and is parallel to $\vec{c} = -4\hat{i} - 6\hat{j} - 2\hat{k}$.Let $\vec{a} = 4\hat{i} - 2\hat{j} + 2\hat{k}

Vedclass · Accepted Answer

$2023$

Vedclass · Answer

(D) The line passes through $A(4, -2, 2)$ and is parallel to $\vec{c} = -4\hat{i} - 6\hat{j} - 2\hat{k}$.Let $\vec{a} = 4\hat{i} - 2\hat{j} + 2\hat{k}$ and $\vec{b} = 2\hat{i} + 1\hat{j} - 3\hat{k}$.The vector $\vec{AB} = \vec{b} - \vec{a} = (2-4)\hat{i} + (1 - (-2))\hat{j} + (-3-2)\hat{k} = -2\hat{i} + 3\hat{j} - 5\hat{k}$.The distance $x$ is given by $\frac{|\vec{AB} 	imes \vec{c}|}{|\vec{c}|}$.$\vec{AB} 	imes \vec{c} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ -2 & 3 & -5 \ -4 & -6 & -2 \end{vmatrix} = \hat{i}(-6 - 30) - \hat{j}(4 - 20) + \hat{k}(12 + 12) = -36\hat{i} + 16\hat{j} + 24\hat{k}$.$|\vec{AB} 	imes \vec{c}| = \sqrt{(-36)^2 + 16^2 + 24^2} = \sqrt{1296 + 256 + 576} = \sqrt{2128}$.$|\vec{c}| = \sqrt{(-4)^2 + (-6)^2 + (-2)^2} = \sqrt{16 + 36 + 4} = \sqrt{56}$.$x^2 = \frac{2128}{56} = 38$.$x^4 + x^2 + 541 = (38)^2 + 38 + 541 = 1444 + 38 + 541 = 2023$.

If the distance of point $B(2, 1, -3)$ from the line passing through the point $A(4, -2, 2)$ and parallel to the vector $\vec{c} = -4\hat{i} - 6\hat{j} - 2\hat{k}$ is $x$, then $x^4 + x^2 + 541 =$

Similar Questions

If $A(-2, 4, a)$,$B(1, b, 3)$,$C(c, 0, 4)$,and $D(-5, 6, 1)$ are collinear points,then $a+b+c=$

$\triangle ABC$ 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

The angle between the pair of lines $\frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4}$ and $\frac{x+1}{1}=\frac{y-4}{4}=\frac{z-5}{2}$ is

Let $L_1: \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $L_2: \frac{x-2}{3}=\frac{y-4}{4}=\frac{z-5}{5}$ be two lines. Then which of the following points lies on the line of the shortest distance between $L_1$ and $L_2$?

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module