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Prove that ( -> a+ -> b)dot( -> a+ -> c)...

Prove that `( -> a+ -> b)dot( -> a+ -> c)| -> a|^2+| -> b|^2` , if and only if ` -> a , -> b` are perpendicular, given ` -> a!= ->0, -> b!= ->0`

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MODERN PUBLICATION-VECTOR ALGEBRA -EXERCISE 10 (e ) Long Answer Type Questions (I)
  1. If vec(a)=3hat(i)+hat(j)+9hat(k) and vec(b)=hat(i)+lambda hat(j)+3ha...

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  2. Find the scalar product of the following pairs of vectors and the angl...

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  3. Find the scalar product of the following pairs of vectors and the angl...

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  4. Show that the vectors 2 hat i- hat j+ hat k , hat i-3 hat j-5 hat kan...

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  5. The position vectors of the vertices of Delta ABC are : 3hat(i)-4hat(j...

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  6. If |vec(a)+vec(b)|=|vec(a)-vec(b)|, prove that vec(a) and vec(b) ar...

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  7. If vec(a) and vec(b) are perpendicular vectors, show that : (vec(a...

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  8. Prove that ( -> a+ -> b)dot( -> a+ -> c)| -> a|^2+| -> b|^2 , if and o...

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  9. If vec a , vec b ,a n d vec c are unit vectors such that vec a+ vec ...

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  10. Three vectors vec a,vec b and vec c satisfy the condition vec a+vec b+...

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  11. If the vectors vec(a), vec(b) and vec(c ) satisfy the condition vec(a...

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  12. The scalar product of the vector vec a= hat i+ hat j+ hat k with a un...

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  13. Let -> a , -> b and -> c be three vectors such that | -> a|=3,| -...

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  14. If |a|=a and | vec b|=b , prove that ( vec a/( vec a^2)- vec b/(b^2))^...

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  15. If vec(a)=3hat(i)+hat(j)-4hat(k), vec(b)=6hat(i)+5hat(j)-2hat(k) and ...

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  16. Let -> a= hat i+4 hat j+2 hat k , -> b=3 hat i-2 hat j+7 hat k and...

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  17. Let vec a= hat i+4 hat j+2 hat k ,\ \ vec b=3 hat i-\ 2 hat j+7 hat ...

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  18. Let vec a= hat i+4 hat j+2 hat k ,\ \ vec b=3 hat i-\ 2 hat j+7 hat ...

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  19. Vectors vec(a)=hat(i)+hat(j)+hat(k), vec(b)=hat(j)+3hat(k) and vec(c ...

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  20. Let vec a= hat i- hat j ,\ vec b=3 hat j- hat k\ a n d\ vec c=7 hat...

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