JEE MATHEMATICS MCQ: STRAIGHT LINES

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Application +4 | -1

O

is the origin and

P\left( {{x_1},{y_1}} \right),Q\left( {{x_2},{y_2}} \right)

are two points, then

OP.OQ\sin \angle POQ =

View answer and explanation

Correct option: C

\left| {{x_1}{y_2} - {x_2}{y_1}} \right|

Option C (

\left| {{x_1}{y_2} - {x_2}{y_1}} \right|

) is correct because it represents the magnitude of the determinant, which is geometrically interpreted as the area of the parallelogram formed by the vectors OP and OQ.

More Questions from STRAIGHT LINES

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If the three lines

x-3 y=p, a x+2 y=q

and

a x+y=r

form a right-angled triangle then :
The orthocentre of the triangle whose vertices are

\left\{ {a{t_1}{t_2},\;a\left( {{t_1} + {t_2})\} ,\{ a{t_2}{t_3},a({t_2} + {t_3}} \right)} \right\},\;\left\{ {a{t_3}{t_1},\;a\left( {{t_3} + {t_1}} \right)} \right\}

is
The distance between the parallel lines

y = 2\;x + 4

and

6x = 3y + 5

is The distance between the pair of lines given by

{x^2} + {y^2} + 2xy - 8ax - 8ay - 9{a^2} = 0

is Find the image of the point

(3,8)

with respect of the line

x+3 y=7

assuming the line to be plane mirror: The centroid of the triangle whose three sides are given by the combined equation

\left( {{x^2} + 7xy + 2{y^2}} \right)\left( {y - 1} \right) = 0