(A) The distance $PQ$ between the two particles is given by the distance formula: $PQ = \sqrt{((t+1) - t)^2 + ((t^3 - 6t - 6) - (t^3 - 16t - 3))^2}$ $

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

(A) The distance $PQ$ between the two particles is given by the distance formula: $PQ = \sqrt{((t+1) - t)^2 + ((t^3 - 6t - 6) - (t^3 - 16t - 3))^2}$ $PQ = \sqrt{(1)^2 + (t^3 - 6t - 6 - t^3 + 16t + 3)^2}$ $PQ = \sqrt{1 + (10t - 3)^2}$ To find the minimum distance, we minimize $PQ^2 = 1 + (10t - 3)^2$. Since $(10t - 3)^2 \geq 0$ for all real $t$, the minimum value of $(10t - 3)^2$ is $0$ when $10t - 3 = 0$, i.e.,$t = 0.3$. Thus, the minimum distance is $\sqrt{1 + 0} = 1$.

Class 11 Mathematics Straight Line System of co-ordinates, Distance between two points, Section formulae

Easy

Two particles $P$ and $Q$ located at the points with coordinates $P(t, t^3-16t-3)$ and $Q(t+1, t^3-6t-6)$ are moving in a plane. The minimum distance between them in their motion is

TS EAMCET 2015 All TS EAMCET

A
$1$
B
$5$
C
$169$
D
$49$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Straight Line

Subtopic

System of co-ordinates, Distance between two points, Section formulae

Previous Year

TS EAMCET 2015 Paper All TS EAMCET years →

Three points $P, Q,$ and $R$ lie on the line segment joining points $A(-6, 8)$ and $B(8, -6)$ such that $AP = PQ = QR = RB$. Find the coordinates of $R$.

Medium

View Solution

If the coordinates of two opposite vertices of a square are $(a, b)$ and $(b, a)$,find the area of the square.

Easy

View Solution

If the polar coordinates of a point are $\left(\sqrt{2}, \frac{\pi}{4}\right)$,then its Cartesian coordinates are

EasyMHT CET 2021

View Solution

Find the coordinates of the point which divides the line segment joining the points $(a + b, a - b)$ and $(a - b, a + b)$ externally in the ratio $a : b$.

Easy

View Solution

$A (-3, 4)$ and $B (2, 1)$ are two given points. If $C$ is a point on $AB$ such that $AC = 2BC$,find the coordinates of $C$.

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Two particles $P$ and $Q$ located at the points with coordinates $P(t, t^3-16t-3)$ and $Q(t+1, t^3-6t-6)$ are moving in a plane. The minimum distance between them in their motion is

Similar Questions

Three points $P, Q,$ and $R$ lie on the line segment joining points $A(-6, 8)$ and $B(8, -6)$ such that $AP = PQ = QR = RB$. Find the coordinates of $R$.

If the coordinates of two opposite vertices of a square are $(a, b)$ and $(b, a)$,find the area of the square.

If the polar coordinates of a point are $\left(\sqrt{2}, \frac{\pi}{4}\right)$,then its Cartesian coordinates are

Find the coordinates of the point which divides the line segment joining the points $(a + b, a - b)$ and $(a - b, a + b)$ externally in the ratio $a : b$.

$A (-3, 4)$ and $B (2, 1)$ are two given points. If $C$ is a point on $AB$ such that $AC = 2BC$,find the coordinates of $C$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module