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If with reference to a right handed syst...

If with reference to a right handed system of mutually perpendicular unit vectors ` hat i ,\ hat j ,\ hat k` we have ` vecalpha=3 hat i- hat j ,\ a n d\ vecbeta=2 hat i+ hat j-3 hat kdot` Express ` vecbeta` in the form ` vecbeta= vecbeta_1+ vecbeta_2,\ w h e r e\ vecbeta_1` is parallel to ` vecalpha\ a n d\ vecbeta_2` is perpendicular to ` vecalphadot`

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The correct Answer is:
`=(1)/(2)(hat(i)+3hat(j)-6hat(k))`
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If with reference to a right handed system of mutually perpendicular unit vectors hat i,hat j,hat k we have vec alpha=3hat i-hat j, and vec beta=2hat i+hat j-3hat k Express vec beta in the form vec beta=vec beta_(1)+vec beta_(2), where vec beta_(1) is parallel to vec alpha and vec beta_(2) is perpendicular to vec alpha .

For mutually perpendicular unit vectors hat(i), hat(j), hat(k) , we have :

If with reference to the right handed system of mutually perpendicular unit vectors hat i , hat j and hat k , ->alpha=3 hat i- hat j , ->beta=2 hat i+ hat j-3 hat k , then express ->beta in the from ->beta= ->beta_1+ ->beta_2 , where -

Let vecalpha = 3hati + hatj and beta= 2hati - hatj + 3hatk . If vecbeta = vecbeta_(1) - vecbeta_(2) , where vecbeta_(1) is parallel to vecalpha and vecbeta_(2) is perpendicular to vecalpha , then vecbeta_(1) xx vecbeta_(2) is equal to:

The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and vec B = hat i - hat j + hat k is

Find a unit vector perpendicular to each of the vectors vec a+ vec b\ a n d\ vec a- vec b ,\ w h e r e\ vec a=3 hat i+2 hat j+2 hat k\ a n d\ vec b= hat i+2 hat j-2 hat kdot

Find vec a.( vec bxx vec c)\ if\ vec a=2 hat i+ hat j+3 hat k ,\ vec b=- hat i+2 hat j+ hat k\ a n d\ vec c=3 hat i+ hat j+2 hat kdot

Find the values of a for which are vectors vecalpha= hat i+2 hat j+ hat k , vecbeta=a hat i+ hat j+2 hat k\ a n d\ vecgamma= hat i+2 hat j+a hat k are coplanar. \

Write a unit vector perpendicular to hat i+ hat j\ a n d\ hat j+ hat kdot

Find a unit vector perpendicular to each of the vector -> a+ -> b and -> a- -> b where -> a=3 hat i+2 hat j+2 hat k and -> b= hat i+2 hat j-2 hat k

MODERN PUBLICATION-VECTOR ALGEBRA -Frequently Asked Questions (Example)
  1. If vec(a) , vec(b) and vec(c ) be three vectors such that vec(a) + vec...

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  2. Three vectors vec(A) = 2hat(i) - hat(j) + hat(k), vec(B) = hat(i) - 3h...

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  3. If vec a ,\ vec b ,\ vec c are three mutually perpendicular vectors...

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  4. Find a vector vec a of magnitude 5sqrt(2) making an angle pi/4 with x-...

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  5. Let vec(A)=4hat(i)+5hat(j)-hat(k), vec(b)=hat(i)-4hat(j)+5hat(k) and v...

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  6. If with reference to a right handed system of mutually perpendicula...

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  7. If vectors vec a\ a n d\ vec b\ are such that | vec a|=3,\ | vec b|...

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  8. If 'theta' is the angle between the vectors : vec(a)=hat(i)+2hat(j)+3h...

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  9. Find 'lambda' and 'mu' if : (hat(i)+3hat(j)+9hat(k))xx(3hat(i)-lam...

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  10. If vec a= hat i+ hat j+ hat kand vec b= hat j- hat k ,find a vect...

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  11. If vec(r )=x hat(i)+y hat(j)+x hat(k), find : (vec(r )xx hat(i)).(vec...

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  12. If vec(a) xx vec(b)= vec(c) xx vec(d) and vec(a) xx vec(c) =vec(b) xx ...

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  13. Find a vector of magnitude 7 units, which is perpendicular to two vect...

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  14. Find the area of the parallelogram whose adjacent sides are determined...

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  15. Find the area of a parallelogram whose adjacent sides are given by th...

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  16. Find the area of a triangle having the pointsA(1, 1, 1), B(1, 2, 3)and...

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  17. If vec(a)=2hat(i)-3hat(j)+4hat(k) and vec(b)=5hat(i)+hat(j)-hat(k) r...

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  18. If vec(a), vec(b), vec(c ) are the position vectors of the vecrtices A...

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  19. Largange's Identify. Prove that (vec(a)xx vec(b))^(2)=|vec(a)|^(2)|vec...

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  20. Show that vec(a)xx vec(b)=vec(a)xx vec(c ) does not imply vec(b)=vec(c...

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