Two non-vertical line with slopes `m_(1) and m_(2)` are perpendicular if and only if `m_(1)timesm_(2)`=___.

Statement 1: The equation of the sides of a triangle are x-3y=0,4x+3y=5 and 3x+y=0. The line 3x-3y=0 passes through the orthocentre of triangle.Statement 2: If two lines of slope m_(1) and m_(2) are perpendicular, then m_(1)m_(2)=-1

Two particles of mass m_(1) "and" m_(2) are in space at separation vecr [vector from m(1) to m_(2) ]. The only force that the two particles experience is the mutual gravitational pull. The force applied by m_(1) "on" m_(2) "is" vecF . Prove that mu(d^(2)vecr)/(dt^(2)) = vecF where mu"(m_(1)m_(2))/(m_(1) + m_(2)) is known as reduced mass for the two particle system .

Two heavy particles having masses m_(1) and m_(2) are situated in a plane perendicular to line AB at a distance or r_(1) and r_(2) respectively. a. What is the moment of inertia of the system about axis AB ? b. What is the moment of inertia of the system about an axis passing through m_(1) and perpendicular to the line joining m_(1) and m_(2) ? c. What is the moment of inertia of the system about an axis passing through m_(1) and m_(2) ?

Two heavy particles having masses m_(1) and m_(2) are situated in a plane perendicular to line AB at a distance or r_(1) and r_(2) respectively. a. What is the moment of inertia of the system about axis AB ? b. What is the moment of inertia of the system about an axis passing through m_(1) and perpendicular to the line joining m_(1) and m_(2) ? c. What is the moment of inertia of the system about an axis passing through m_(1) and m_(2) ?

STATEMENT-1: The straight lines 2x+3y+5=0and 3x-2y+1=0 are perpendicular to each other. STATEMENT-2: Two lines y=m_(1)x+c_(1)and y=m_(2)x+c_(2) where m_(1),m_(2)in R are perpendicular if m_(1),m_(2)=-1. STATEMENT-2: Two lines y=m_(1)xx+x_(1)and y=m_(2)x+c_(2)where m_(1),m_(2)inR are peprendicular if m_(1)m_(2)=-1.

STATEMENT-1: The straight lines 2x+3y+5=0and 3x-2y+1=0 are perpendicular to each other. STATEMENT-2: Two lines y=m_(1)x+c_(1)and y=m_(2)x+c_(2) where m_(1),m_(2)in R are perpendicular if m_(1),m_(2)=-1. STATEMENT-2: Two lines y=m_(1)xx+x_(1)and y=m_(2)x+c_(2)where m_(1),m_(2)inR are peprendicular if m_(1)m_(2)=-1.

If theta is the angle between two lines whose d.c's are (l_(1),m_(1),n_(1)) and (l_(2),m_(2),n_(2)) then the lines are perpendicular if and only if

Derive a formula for the angle between two lines with slopes m_(1) and m_(2) . Hence the slopes of the lines which make an angle pi/4 with the line x-2y+5=0

Two heavy particles having masses m_(1) & m_(2) are situated in a plane perpendicular to line AB at a distance of r_(1) and r_(2) respectively . What is the moment of inertia of the stystem about axis AB ?