An equilateral triangle has each of its ...

An equilateral triangle has each of its sides of length 6 cm. If `(x_1, y_1);(x_2, y_2)&(x_3, y_3)` are its vertices, then the value of the determinant `|x_1y_1 1x_2y_2 1x_3y_3 1|^2` is equal to: 192 (b) 243 (c) 486 (d) 972

Text Solution

AI Generated Solution

Topper's Solved these Questions

COMPOUND ANGLES
ALLEN|Exercise EX -JA|8 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
ALLEN|Exercise All Questions|147 Videos

Similar Questions

Explore conceptually related problems

An equilateral triangle has each of its sides of length 6 cm. If (x_(1),y_(1)), (x_(2),y_(2)) & (x_(3),y_(3)) are the verticles, then the value of the determinant |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|^(2) is equal to :

An equilateral triangle has each of its sides of length 4 cm. If (x_(r),y_(r)) (r=1,2,3) are its vertices the value of |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|^2

An equilateral triangle has each side to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinat |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)| equals

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

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

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

Write the formula for the area of the triangle having its vertices at (x_1,\ y_1),\ \ (x_2,\ y_2) and (x_3,\ y_3) .

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 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

If the coordinates of the vertices of an equilateral triangle with sides of length a are (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) then |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2=(3a^(4))/4

ALLEN-DETERMINANTS-All Questions

If f(x)=|(1, x, x+1), (2x, x(x-1), (x+1)x), (3x(x-1), x(x-1)(x-2), (x+...
Text Solution
|
The value of the determinant |{:(a, b,0), (0,a, b),(b,0,a):}| is equal...
Text Solution
|
An equilateral triangle has each of its sides of length 6 cm. If (x1, ...
Text Solution
|
If the system of equations x + 2y + 3z = 4, x+ py+ 2z = 3, x+ 4y +u z ...
Text Solution
|
The maximum value of Δ= ∣ ∣ ∣ 1 1 1+cosθ 1 1+sinθ 1 1...
Text Solution
|
If f^(prime)(x)=|[mx, mx-p, m x+p], [n, n+p, n-p], [mx+2n, m x+2n+p, m...
Text Solution
|
The determinant |a b aalpha+bb c balpha+c aalpha+bbalpha+c0|=0, if a ...
Text Solution
|
Let f(x)=|1+sin^2x cos^2x4s in2xsin^2\ \ x1+cos^2x4s in2xsin^2xcos^...
Text Solution
|
The parameter on which the value of the determinant |[1,a...
Text Solution
|
If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...
Text Solution
|
Given that q^2-p r ,0,\ p >0, then the value of |p q p x+q y q r...
Text Solution
|
The values of θ lying between 0 and π/2 and satisfying the equation ...
Text Solution
|
If |(a, a, x,),(m, m, m),(b, x, b)|=0 then x may be equal to- a.a b. ...
Text Solution
|
If ∣ -a a^2 ab ac ab -b^2 bc ac bc -c^2 | = ka^2b^2c^2...
Text Solution
|
The value of the determinant |(alpha,beta,l),(alpha,x, n),(alpha,beta,...
Text Solution
|
If the system of linear equations x+a y+a z=0,\ x+b y+b z=0,\ x+c y+...
Text Solution
|
If the system of equations x+y-3=0,\ (1+K)x+(2+K)y-8=0\ &\ x-(1+K)y+(2...
Text Solution
|
If the determinant |a+p l+x u+fb+q x+y v+gc+r n+z w+h| splits into exa...
Text Solution
|
The values of lambda for which the system of euations x+y+z=6x+2y+3z=1...
Text Solution
|
If x , y , z are in A.P. , then the value of the determinant are in A....
Text Solution
|