If (x1-x2)^2+(y1-y2)^2=a^2, (x2-x3)^2+(...

If `(x_1-x_2)^2+(y_1-y_2)^2=a^2`, `(x_2-x_3)^2+(y_2-y_3)^2=b^2`, `(x_3-x_1)^2+(y_3-y_1)^2=c^2`, and `2s=a+b+c` then what willl be the value of `1/4|[x_1,y_1, 1],[x_2,y_2, 1],[x_3,y_3, 1]|^2`

`s(s-a)^(2)`

`(s-b)(s-c)^(2)`

`s(s-a)(s-b)(s-c)`

None of these

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

STRAIGHT LINES
VMC MODULES ENGLISH|Exercise Level -2|43 Videos
STRAIGHT LINES
VMC MODULES ENGLISH|Exercise Level -2 Passage|5 Videos
STRAIGHT LINES
VMC MODULES ENGLISH|Exercise Level - 0 (True or False)|7 Videos
SEQUENCE AND SERIES
VMC MODULES ENGLISH|Exercise JEE MAIN & Advance ( ARCHIVE)|46 Videos
THREE DIMENSIONAL GEOMETRY
VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|34 Videos

Similar Questions

Explore conceptually related problems

If (x_1-x_2)^2+(y_1-y_2)^2=144 ,(x_2-x_3)^2+(y_2-y_3)^2=25 and (x_3-x_1)^2+(y_3-y_1)^2=169 , then the value of |[x_1,y_1, 1],[x_2,y_2 ,1],[x_3,y_3, 1]|^2 is 30 (b) 30^2 (c) 60 (d) 60^2

if (x_(1)-x_(2))^(2)+(y_(1)-y_(2))^(2)=a^(2), (x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=b^(2) (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=c^(2). where a,b,c are positive then prove that 4 |{:(x_(1),,y_(1),,1),(x_(2) ,,y_(2),,1),( x_(3),, y_(3),,1):}| = (a+b+c) (b+c-a) (c+a-b)(a+b-c)

If A(x_1, y_1),B(x_2, y_2) and C(x_3,y_3) are vertices of an equilateral triangle whose each side is equal to a , then prove that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=3a^4

If a x_1^2+b y_1^2+c z_1^2=a x_2 ^2+b y_2 ^2+c z_2 ^2=a x_3 ^2+b y_3 ^2+c z_3 ^2=d ,a x_2 x_3+b y_2y_3+c z_2z_3=a x_3x_1+b y_3y_1+c z_3z_1=a x_1x_2+b y_1y_2+c z_1z_2=f, then prove that |(x_1, y_1, z_1), (x_2, y_2, z_2), (x_3,y_3,z_3)|=(d-f){((d+2f))/(a b c)}^(1//2)

If (x_i,y_i),i=1,2,3 are the vertices of an equilateral triangle such that (x_1+2)^2+(y_1-3)^2=(x_2+2)^2+(y_2-3)^2=(x_3+2)^2+(y_3-3)^2 , then find the value of (x_1+x_2+x_3)/(y_1+y_2+y_3)

If [x+y x-y]=[2 1 4 3][1-2] , then write the value of (x ,\ y) .

If (x_i ,y_i),i=1,2,3, are the vertices of an equilateral triangle such that (x_1+2)^2+(y_1-3)^2=(x_2+2)^2+(y_2-3)^2=(x_3+2)^2+(y_3-3)^2, then find the value of (x_1+x_2+x_3)/(y_1+y_2+y_3) .

If A(x_1, y_1),B(x_2, y_2)a n dC(x_3,y_3) are vertices of an equilateral triangle whose each side is equal to a , then prove that |(x_1,y_1, 2),(x_2,y_2, 2),(x_3,y_3, 2)|^2=3a^4

Write the condition of collinearity of points (x_1,\ y_1),\ \ (x_2,\ y_2) and (x_3,\ y_3) .

If the points (x_1,y_1),(x_2,y_2)and(x_3,y_3) are collinear, then the rank of the matrix {:[(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)]:} will always be less than

VMC MODULES ENGLISH-STRAIGHT LINES-Level -1

The vertices of a triangle are (A(-1,-7),B(5,1), and C(1,4)dot The equ...
Text Solution
|
The coordinates of points A,B,C and D are (-3, 5), (4, -2), (x, 3x) an...
Text Solution
|
If (x1-x2)^2+(y1-y2)^2=a^2, (x2-x3)^2+(y2-y3)^2=b^2, (x3-x1)^2+(y3-y1...
Text Solution
|
The point P(a,b) lies on the straight line 3x+2y=13 and the point Q(b,...
Text Solution
|
If the lines x(sinalpha+sinbeta)-ysin(alpha-beta)=3 and x(cosalpha+c...
Text Solution
|
The vertex C of a triangle ABC moves on the line L-=3x+4y+5=0. The c...
Text Solution
|
Line L has intercepts aa n db on the coordinate axes. When the axes ar...
Text Solution
|
The point (alpha^(2)+2lamda+5,lamda^(2)+1) lies on the line x+y=10 ...
Text Solution
|
The straight line passing through the point of intersection of the str...
Text Solution
|
The base BC of a triangle ABC is bisected at the point (a, b) and equa...
Text Solution
|
the image of the point A(2,3) by the line mirror y=x is the point B a...
Text Solution
|
A point equidistant from the line 4x+3y+10=0,\ 5x-12 y+26=0\ a n d\ 7x...
Text Solution
|
The bisector of the acute angle formed between the lines 4x - 3y + 7 ...
Text Solution
|
The straight line through P(x1, y1) inclined at an angle theta with th...
Text Solution
|
Find the equation of the line through (2,3) so that the segment of the...
Text Solution
|
A straight line through the point (2,2) intersects the lines sqrt(3)x+...
Text Solution
|
Consider the equation y-y1=m(x-x1) . If ma n dx1 are fixed and differe...
Text Solution
|
The equation of line on which the perpendicular from the origin make 3...
Text Solution
|
If the point A is symmetric to the point B(4,-1) with respect to the ...
Text Solution
|
The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent...
Text Solution
|