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Show that: |[a, b-c,c+b], [a+c, b, c-a]...

Show that: `|[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]|`=`(a+b+c)(a^2+b^2+c^2)dot`

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Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b+b c+c a)dot

Show that |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|=2(a+b+c)^3 .

Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-c^3dot

Using properties of determinant prove that |[a+b+c,-c,-b],[-c, a+b+c,-a],[-b,-a, a+b+c]|=2(a+b)(b+c)(c+a)

Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c)(c+a)

Prove that, |(2a, a-b-c,2a),(2b,2b,b-c-a),(c-a-b,2c,2c)|=(a + b+c)^3

Show that , |[(a^2+b^2)/c,c,c],[a,(b^2+c^2)/a,a],[b,b,(c^2+a^2)/b]|=4abc

Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)(c- a)

If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ,b ,c in R) and are all different and nonzero), then prove that a+b+c=0.

Show that: abs(((b+c)^2,a^2,bc) , ((c+a)^2,b^2,ca) , ((a+b)^2,c^2,ab))=(a^2+b^2+c^2)(a+b+c)(b-c)(c-a)(a-b)

UNITED BOOK HOUSE-SET 17-EXERCISE
  1. Eleminating a and b, find the differential equation of all ellipse of ...

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  2. Evaluate : underset(x rarr 0) Lt (1+3x)^((x+2)/x)

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  3. If vec a, vec b, vec c are unit vectors satisfying the condition veca+...

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  4. Find the value of lambda so that the plane vecr. (veci + 2vecj + 3veck...

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  5. If P(A)=1/4,P(B)=1/3 and P(A-B)=1/6 then verify whether a and B are tw...

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  6. An unbiased coin is tossed 6 times. Find the probability of at least f...

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  7. Given A =[(1,-1,1),(1,-2,-2),(2,1,3)] & B = [(-4,4,4),(-7,1,3),(5 , -3...

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  8. Show that: |[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]|=(a+b+c)(a^2+b^2...

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  9. Show that int(2x+3)/(x^2 - 3x + 2) dx

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  10. If x = sin theta and y = cos ptheta , p is constant, then find the val...

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  11. The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitr...

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  12. Show that int(2x+3)/(x^2 - 3x + 2) dx

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  13. If theta be the angle between two unit vectors vece1 and vece2 then pr...

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  14. Evaluate (with the help of definite integral) underset(nrarr infty) ...

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  15. Find the value of overset(pi//2)underset(0)int (1 )/((b^2 cos^2 x + a^...

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  16. A mawn takes a step forward with probability 0.4 and backward with pro...

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  17. A card from a pack of 52 cards is lost. From the remaining cards of ...

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  18. If the area of the region {(x , y):0lt=ylt=x^2+1,0lt=ylt=x+1,0lt=xlt=2...

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  19. (b)answer any two questions : (i) a circular ink blot grows at the rat...

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  20. Find the distance of the point (1,-2,3) from the plane x - y +z = 5 me...

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