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The value of |2x1y1x1y2+x2y1x1y3+x3y1x1y...

The value of `|2x_1y_1x_1y_2+x_2y_1x_1y_3+x_3y_1x_1y_2+x_2y_1 2x_2y_2x_2y_3+x_3y_2x_1y_3+x_3y_1x_2y_3+x_3y_2 2x _3y_3|` is.

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The value of |(1,1,1),(2x,2y,2z),(3x,3y,3z)| is ____

3x+y=1,2x=11y+3

3x-y=2,5x-2y=1

A triangle has vertices A_i(x_i , y_i)fori=1,2,3 If the orthocentre of triangle is (0,0), then prove that |x_2-x_3y_2-y_3y_1(y_2-y_3)+x_1(x_2-x_3)x_3-x_1y_2-y_3y_2(y_3-y_1)+x_1(x_3-x_1)x_1-x_2y_2-y_3y_3(y_1-y_2)+x_1(x_1-x_2)|=0

If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 at four points P(x_1, y_1),Q(x_2, y_2),R(x_3, y_3), and S(x_4, y_4), then x_1+x_2+x_3+x_4=0 y_1+y_2+y_3+y_4=0 x_1x_2x_3x_4=C^4 y_1y_2y_3y_4=C^4

x+2y=-1,2x-3y=12

The line 2x+3y=5 , 2x+y=k , 2x-y-1=0

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If the normals to the ellipse x^2/a^2+y^2/b^2= 1 at the points (X_1, y_1), (x_2, y_2) and (x_3, y_3) are concurrent, prove that |(x_1,y_1,x_1y_1),(x_2,y_2,x_2y_2),(x_3,y_3,x_3y_3)|=0 .

If a x1 2+b y1 2+c z1 2=a x2 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d ,a x2 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_1y_1z_1x_2y_2z_2x_3y_3z_3|=(d-f){((d+2f))/(a b c)}^(1//2)

CENGAGE-DETERMINANTS-All Questions
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