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What is abs(veca-vecb)=if abs(veca)=3,ab...

What is `abs(veca-vecb)=if abs(veca)=3,abs(vecb)=4` and `abs(veca+vecb)=5`?

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What is the angle between veca and vecb if abs(veca+vecb)=abs(veca-vecb) ?

Prove that |veca xx vecb|^(2) = abs(veca)^(2)abs(vecb)^(2) - (veca * vecb)^(2)

Let veca,vecb,vecc be three vectors such that veca+vecb+vecc=vec0 and abs(veca)=3,abs(vecb)=5,abs(vecc)=7 . Then prove that the angle between veca and vecb is 60^@ .

If abs(veca)=3,abs( vecb)=1,abs(vecc)=4 and veca+vecb+vecc=0, find the value of veca*vecb+vecb*vecc+vecc*veca.

Show that (vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2 .

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Prove that (veca.vecb)^2=a^2b^2-(veca xx vecb)^2

If abs(veca+vecb)=abs(veca-vecb) then what is the angle between veca and vecb ?

Let the vectors veca and vecb such that abs(veca)=3 and abs(vecb)=frac[sqrt2][3] . If vecatimesvecb is a unit vector, then find the angle between veca and vecb .

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. What is the antiderivative of 5^(5+x)?

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  2. What is the order of the matrix B if [2 3 5 -1] B=[1 3 2 5 -4 1] .

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  3. What is abs(veca-vecb)=if abs(veca)=3,abs(vecb)=4 and abs(veca+vecb)=5...

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  4. Find the principal value of sin^1(sin"(2pi)/3)

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  5. What is the value of d/dxint150^300(x^3+3x^2)^3dx ?

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  6. What is the value of d/dx[lnsin^(-1){cos((pi-2e^x)/2)}] ?

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  7. Let f= {(1,3),(2,4),(3,7)} and g ={(3,2),(4,3),(7,1)} Determine gof ...

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  8. If y=sinx+cosx then what is [dy/dx]^2.

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  9. Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B))...

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  10. Find the maximum value of Z = 2x + 3y subject to conditions x+ yle1 an...

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  11. Prove that sin^(-1)(frac[sqrt(1+x)+sqrt(1-x)][2])=frac[pi][4]+frac[1][...

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  12. Show that the relation ~ on ZZ-{0}timesZZ-{0} defined by (m,n)~(p,q)Le...

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  13. Solve by matrix method. 2x + y = 5 , x-y =1

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  14. If A=[[(1,1)],[(1,1)]] and n inN, then A^n=2^(n-1)A .

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  15. If [[(x,y)],[(x,x/2+x)]]+[[(y,x+t)],[(x/2,x/2)]]=[[(1,4)],[(2,2)]] the...

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  16. Evaluate the determinant abs((4,6,-2),(1,-4,3),(7,-2,1)

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  17. If abs((a,b,a-b),(b,c,b-c),(2,1,0))=0 , then prove that a,b,c are in G...

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  18. evaluate lim(xto1)(x^2-3x+2)/(x-1) .

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  19. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2 then prove that x^3ydy/dx=1.

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  20. Find the maximum and minimum of f(x)=|x+3|,for all x belongs to R.

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