The area of the parallelogram formed by the l | vedclass

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

Question

(D) Given lines are $L_1: \lambda x+4 y+2=0$,$L_2: 3 x+4 y-3=0$,$L_3: 2 x+\mu y+6=0$,$L_4: 2 x+y+3=0$. Since $L_1 \parallel L_2$,their slopes must be

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) Given lines are $L_1: \lambda x+4 y+2=0$,$L_2: 3 x+4 y-3=0$,$L_3: 2 x+\mu y+6=0$,$L_4: 2 x+y+3=0$. Since $L_1 \parallel L_2$,their slopes must be equal: $-\frac{\lambda}{4} = -\frac{3}{4} \Rightarrow \lambda = 3$. Since $L_3 \parallel L_4$,their slopes must be equal: $-\frac{2}{\mu} = -\frac{2}{1} \Rightarrow \mu = 1$. The area of a parallelogram formed by lines $a_1 x+b_1 y+c_1=0$,$a_1 x+b_1 y+c_2=0$,$a_2 x+b_2 y+d_1=0$,and $a_2 x+b_2 y+d_2=0$ is given by $\frac{|(c_1-c_2)(d_1-d_2)|}{|a_1 b_2 - a_2 b_1|}$. Here,$L_1: 3x+4y+2=0$,$L_2: 3x+4y-3=0$,$L_3: 2x+y+6=0$,$L_4: 2x+y+3=0$. $c_1=2, c_2=-3, d_1=6, d_2=3$. $a_1=3, b_1=4, a_2=2, b_2=1$. Area $= \frac{|(2 - (-3))(6 - 3)|}{|(3)(1) - (2)(4)|} = \frac{|5 	imes 3|}{|3 - 8|} = \frac{15}{|-5|} = \frac{15}{5} = 3$. Thus,the area is $3$ square units.

The area of the parallelogram formed by the lines $L_1 \equiv \lambda x+4 y+2=0$,$L_2 \equiv 3 x+4 y-3=0$,$L_3 \equiv 2 x+\mu y+6=0$,and $L_4 \equiv 2 x+y+3=0$,where $L_1$ is parallel to $L_2$ and $L_3$ is parallel to $L_4$,is

Similar Questions

If $A(4,7)$,$B(-7,8)$,and $C(1,2)$ are the vertices of $\triangle ABC$,then the equation of the perpendicular bisector of the side $AB$ is

Two lines are drawn through $(3, 4)$,each of which makes an angle of $45^\circ$ with the line $x - y = 2$. The area of the triangle formed by these lines is:

The sides of a triangle are $3x+2y-6=0$,$2x-3y+6=0$,and $x+2y+2=0$. If $P(0, b)$ lies either on the triangle or inside the triangle,then $b$ lies in the interval

The points $A(2a, 4a)$,$B(2a, 6a)$,and $C(2a + \sqrt{3}a, 5a)$,where $a > 0$,are the vertices of:

If two vertices of an equilateral triangle are $(1, 0)$ and $(3, 0)$,and the third vertex lies in the first quadrant,find the area of the triangle.

Vedclass Test Series

Exam Paper Generator

Online Exam Module