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If `hat(a), hat(b) and hat(c)` are the three unit vector and `alpha, beta and gamma` are scalars such that `hat(c)=alphahat(a)+betahat(b)+gamma(hat(a)xxhat(b)).` If is given that `hat(a)*hat(b)=o and hatc` makes equal angle with both `hat(a)and hat(b)`, then evaluate `alpha^(2)+beta^(2)+gamma^(2)`.

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ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (Single Integer Answer Type Questions)
  1. Let hat(u), hat(v) and hat(w) are three unit vectors, the angle betwee...

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  2. If a, b and c are three vectors such that [a b c]=1, then find the val...

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  3. If hat(a), hat(b) and hat(c) are the three unit vector and alpha, bet...

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  4. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

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  5. Let hatc be a unit vector coplanar with a=hat(i)-hat(j)+2hat(k) and b...

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  6. Let a, b and c are three vectors hacing magnitude 1, 2 and 3 respectiv...

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  7. Let A(2hat(i)+3hat(j)+5hat(k)), B(-hat(i)+3hat(j)+2hat(k)) and C(lambd...

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  8. If V is the volume of the parallelopiped having three coterminus edges...

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  9. If veca,vecb are vectors perpendicular to each other and |veca|=2, |ve...

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  10. M and N are mid-point of the diagnols AC and BD respectivley of quadri...

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  11. If atimesb=c, btimesc=a, ctimesa=b. If vectors a, b and c are forming ...

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  12. Let veca and vecc be unit vectors inclined at pi//3 with each other. I...

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  13. Volume of parallelopiped formed by vectors vecaxxvecb, vecbxxvecc and ...

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  14. If alpha and beta are two perpendicular unit vectors such that x=hat(b...

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  15. The volume of the tetrahedron whose vertices are the points with posit...

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  16. The volume of a tetrahedron formed by the coterminous edges vec a ...

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