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If the determinant of the matrix [(a(...

If the determinant of the matrix `[(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))]` is denoted by D, then the determinant of the matrix `[(a_(1)+3b_(1)-4c_(1),b_(1),4c_(1)),(a_(2)+3b_(2)-4c_(2),b_(2),4c_(2)),(a_(3)+3b_(3)-4c_(3),b_(3),4c_(3))]` will be -

A

D

B

2D

C

3D

D

4D

Text Solution

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The correct Answer is:
D
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Find the coordinates of the centriod of the triangle whose vertices are ( a_(1), b_(1), c_(1)) , (a_(2), b_(2), c_(2)) and (a_(3), b_(3), c_(3)) .

If x in R,a_(i),b_(i),c_(i) in R for i=1,2,3 and |{:(a_(1)+b_(1)x,a_(1)x+b_(1),c_(1)),(a_(2)+b_(2)x,a_(2)x+b_(2),c_(2)),(a_(3)+b_(3)x,a_(3)x+b_(3),c_(3)):}|=0 , then which of the following may be true ?

Represent the following equations in matrix form: a_(1)x+b_(1)y+c_(1)z=k_(1) a_(2)x+b_(2)y+c_(2)z=k_(2) a_(3)x+b_(3)y+c_(3)z=k_(3)

Represent the following linear equations in matrix form: a_(1)x+b_(1)y+c_(1)z+d_(1)=0 , a_(2)x+b_(2)y+c_(2)z+d_(2)=0 and a_(3)x+b_(3)y_+c_(3)z+d_(3)=0

Represent the following equations in matrix form: a_(1)x+b_(1)y+c_(1)=0 a_(2)x+b_(2)y+c_(2)=0

Applying vectors , show that (a_(1)b_(1)+a_(2)b_(2)+a_(3)b_(3))^(2)le (a_(1)^(2)+a_(2)^(2)+a_(3)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(2))

If D= |{:(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3):}| and A_1,B_1,C_1 etc. are the respective cofactors of the elements a_1,b_1,c_1 etc. then D will be-

If the straight lines a_(1)x+b_(1)y+c=0,a_(2)x+b_(2)y+c=0anda_(3)x+b_(3)y+c=0[cne0] are concurrent , show that the points (a_(1),b_(1),(a_(2),b_(2))and(a_(3),b_(3)) are collinear.

(2a-3b)^(3)+(4c-2a)^(3)+(3b-4c)^(3)

CHHAYA PUBLICATION-MCQ ZONE -Question Paper 3
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  15. The area of the parallelogram formed by the vectors 3hati-2hatj+hatk ...

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  18. If vec alpha, vec beta, vecgamma be three unit vectors such that |ve...

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