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Show that each of the given three vector...

Show that each of the given three vectors is a unit vector :`1/7(2overset^^i+3overset^^j+6overset^^k),1/7(3overset^^i-6overset^^j+2overset^^k),1/7(6overset^^i+2overset^^j-3overset^^k)`.
Also, show that the are mutually perpendicular to each other.

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V PUBLICATION-VECTOR ALGEBRA-QUESTION BANK
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  2. Find the projection of a vector i+3j+7k on the vector 7i-j+8k.

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  3. Show that each of the given three vectors is a unit vector :1/7(2overs...

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  4. Find |veca| and |vecb|, if (veca+vecb) .(veca-vecb)=8 and |veca|=8|vec...

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  5. Evaluate the product (3 veca-5 vecb) .(2 veca+7 vecb)

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  6. Find the magnitude of two vectors oversetrarra"and"oversetrarrb, havin...

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  7. Find |vecx|, if for a unit vector veca,(vecx-veca) .(vecx+veca)=12'

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  8. If" " oversetrarra=2overset^^i+2overset^^j+3overset^^k," " oversetrarr...

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  9. Show that""|oversetrarra|oversetrarrb +|oversetrarrb| oversetrarra"" i...

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  10. If veca.veca=0 and veca. vecb=0, then what can be concluded about the ...

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  11. If veca, vecb, vecc are unit vectors such that veca+vecb+vecc=0, fin...

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  12. If either veca=vec0"or" vecb =vec0, "then"vecaxxvecb=vec0.Is the conve...

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  13. If the vertices A,B,C of a triangle ABC are (1,2,3),(-1,0,0),(0,1,2)re...

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  14. Using vectors, show that the points A(1,2,7),B(2,6,3),C(3,10,-1) are...

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  15. Show that the vectors 2 hati-hatj+hatk, hati-3 hatj-5 hatk and 3 hati-...

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  16. If a is a non-zero vector of magnitude'a' and lambda a non-zero scala...

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  17. Show that the area of a parallelogram with diagonals veca and vecb is ...

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  18. Find |veca xx vecb| if veca=2 hati+hatj+3 hatk and vecb=3 hati+5 hatj-...

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  19. Find a unit vector perpendicular to each of the vectors (veca +vecb) a...

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  20. Consider the triangle ABC with vertices A(1,1,1), B(1,2,3) and C(2,3,1...

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