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Using properties of determinants, prove that `|(b+c,q+r,y+z),(c+a,r+p,z+x),(c+b,p+q,x+y)|=2|(a,p,x),(b,q,y),(c,r,z)|`

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To prove that \[ \begin{vmatrix} b+c & q+r & y+z \\ c+a & r+p & z+x \\ c+b & p+q & x+y \end{vmatrix} ...
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Use the properties of determinant and without expanding prove that |{:(b+c,q+r,y+z),(c+a,r+p,z+x),(a+b,p+q,x+y):}| = 2 |{:(a,p,x),(b,q,y),(c,r,z):}| .

Using the property of determinants and without expanding, prove that: |b+c q+r y+z c+a r+p z+x a+b p+q x+y|=2|a p x b q y c r z|

Prove that: |{:(a, b, c), (x, y, z), (p, q, r):}|=|{:(y, b, q), (x, a, p), (z, c, r):}|

Without expansion, prove the following: |(a+b, b+c, c+a),(p+q, q+r, r+ p),(x+y, y+z, z+x)|=2|(a,b,c),(p,q,r),(x,y,z)|

Without expanding, prove that : |{:(1+b,b+c,c+a),(p+q,q+r,r+p),(x+y,y+z,z+x),(x+y,y+z,z+x):}|=2|{:(a,b,c),(p,q,r),(x,y,z):}|

Using the property of determinants and without expanding in questions 1 to 7 prove that , |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

Prove that: |[b+c, c+a, a+b],[q+r, r+p, p+q],[y+z, z+x, x+y]|=2|[a,b,c],[p,q,r],[x,y,z]|

If A = |(a,b,c),(x,y,z),(p,q,r)| and B = |(q,-b,y),(-p,a,-x),(r,-c,z)| , then

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Of the students in a college, it is known that 60% reside in hostel...

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  2. Using the method of integration, find the area of the region bounde...

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  3. Using properties of determinants, prove that |(b+c,q+r,y+z),(c+a,r+p,z...

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  4. Find the equation of the plane determined by the points A(3, –1, 2)...

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  5. Let A=R-{3} and B=R-[1]dot Consider the function f: AvecB defined by f...

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  6. Show that the height of a closed right circular cylinder of given s...

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  7. If [(9,-1,4),(-2,1,3)]=A+[(1,2,-1),(0,4,9)], then find the matrix A.

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  8. If |(x+1,x-1),(x-3,x+2)|=|(4,-1),(1,3)|, then write the value of x .

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  9. If vec a=x hat i+2 hat j-\ z hat k and vec b=3 hat i-\ y hat j+ hat ...

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  10. Write the degree of the differential equation x^3((d^2y)/(dx^2))^2+x\ ...

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  11. Prove the following: tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3...

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  12. Find the value of a if [(a-b,2a+c),(2a-b,c+d)]=[(-1,5),(0,13)]

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  13. Prove the following: "cos"{tan^(-1){sin(cot^(-1)x)}}= sqrt((1+x^2)/(...

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  14. Find the Cartesian equation of the line which passes through the po...

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  15. If a unit vector vec a makes angles pi/3 with hat i ,pi/4 with hat ...

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  16. Find | vec x| , if for a unit vector vec a ,\ ( vec x- vec a)*( vec ...

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  17. Find the length of the perpendicular drawn from the origin to the p...

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  18. Find the vector equation of the plane passing through three points ...

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  19. Write the principal value of tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3)) .

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  20. Write the value of tan^(-1)[2sin(2cos^(-1)(sqrt(3/2))] .

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