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|(a,b,c),(a(1),b(1),c(1)),(a(2),b(2),c(2...

`|(a,b,c),(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2))|=k|(b+c,c+a,a+b),(b_(1)+c_(1),c_(1)+a_(1),a_(1)+b_(1)),(b_(2)+c_(2),c_(2)+a_(2),a_(2)+b_(2))|` then `k=`

A

1

B

`1//2`

C

4

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
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A : The area of the parallelogram formed by 4x-7y-13=0, 8x-y-39=0, 4x-7y+39=0, 8x-y+13=0 is 52. R : The area of the parallelogram formed by a_(1)x+b_(1)y+c_(1)=0, a_(1)x+b_(1)y+d_(1)=0, a_(2)x+b_(2)y+c_(2)=0, a_(2)x+b_(2)y+d_(2)=0 is |((c_(1)-d_(1))(c_(2)-d_(2)))/(a_(1)b_(2)-a_(2)b_(1))|

If |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|=|(a_(1),b_(1),1),(a_(2),b_(2),1),(a_(3),b_(3),1)| , then the two triangles with vertices (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) and (a_(1),b_(1)),(a_(2),b_(2)),(a_(3),b_(3)) must be

DIPTI PUBLICATION ( AP EAMET)-MATRICES-EXERCISE 1B MCQ (DETERMINANTS)
  1. If|(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=k|(a,b,c),(b,c,a),(c,a,b...

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  2. |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=

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  3. |(a,b,c),(a(1),b(1),c(1)),(a(2),b(2),c(2))|=k|(b+c,c+a,a+b),(b(1)+c(1)...

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  4. If |(x,y,z),(-x,y,z),(x,-y,z)|=k xyz, then k=

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  5. If D=|(1,1,1),(1,1+x,1),(1,1,1+y)| for x!=0,y!=0 then D is

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  6. |(x,a,a),(a,x,a),(a,a,x)|=

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  7. |(1+a,b,c),(a,1+b,c),(a,b,1+c)|=

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  8. If |(1+a(1),a(2),a(3)),(a(1),1+a(2),a(3)),(a(1),a(2),1+a(3))|=0 then a...

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  9. |(1+a,b,c),(a,1+b,c),(a,b,1+c)|=

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  10. If 1/a+1/b+1/c=0 then |(1+a,1,1),(1,1+b,1),(1,1,1+c)|=

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  11. |(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1)|=

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  12. Show that |{:(a-b-c," "2a," "2a),(" "2b,b-c-a," "2b),(" "2c," "2...

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  13. Show that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3

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  14. A=[(1, 5, 6),(2,3,4),(1,1,1)] find rank of A

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  15. |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=

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  16. |(a^(2)+x,ab,ac),(ab,b^(2)+x,bc),(ac,bc,c^(2)+x)|

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  17. |(a^(2)+2a,2a+1,1),(2a+1,a+2,1),(3,3,1)|

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  18. |(sin^(2)x,cos^(2)x,1),(cos^(2)x,sin^(2)x,1),(-10,12,2)|=

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  19. If A=[a(ij)] is a scalar matrix of order nxxn such that a(ij)=k for al...

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  20. If A=[a(ij)] is a square matrix of order nxxn and k is a scalar then |...

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