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Find lambda, when the projection of vec...

Find `lambda,` when the projection of ` vec a=lambda hat i+ hat j+4 hat k\ on\ vec b=2 hat i+6 hat j+3 hat k\ i s\ 4\ ` units.

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Find lambda, when the projection of vec a=lambdahat i+hat j+4hat k on vec b=2hat i+6hat j+3hat k is 4 units.

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For what value of lambda are the vector vec a and vec b perpendicular to each other? where: vec a=lambda hat i+2 hat j+ hat k and vec b=4 hat i-9 hat j+2 hat k vec a=lambda hat i+2 hat j+ hat k and vec b=5 hat i-9 hat j+2 hat k vec a=2 hat i+3 hat j+4 hat k and vec b=3 hat i+2 hat j-lambda hat k vec a=lambda hat i+3 hat j+2 hat k and vec b= hat i- hat j+3 hat k

find |vec a xxvec b| where vec a=3hat i+4hat j and vec b=hat i+hat j+hat k

Find 'lambda' when the vectors : vec(a)=2hat(i)+lambda hat(j)+hat(k) and vec(b)=hat(i)-2hat(j)+3hat(k) are perpendicular to each other.

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors: vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j+2 hat k vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j-2 hat k vec a=11 hat i , vec b=2 hat j- hat k , vec c=13 hat k vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k

Find vec adot vec b , when (i) vec a= hat i-2 hat j+ hat k and vec b=4 hat i-4 hat j+7 hat k (ii) vec a= hat j+2hat k and vec b = 2 hat i+ hat k (iii) vec a= hat j-hat k andvec b= 2 hat i+3 hat j-2 hat k

The line through hat i+3 hat j+2 hat k and _|_ to the line vec r=( hat i+2 hat j- hat k)+lambda(2 hat i+ hat j+ hat k)a n d vec r=(2 hat i+6 hat j+ hat k)+mu( hat i+2 hat j+3 hat k) is a. vec r=( hat i+2 hat j- hat k)+lambda(- hat i+5 hat j-3 hat k) b. vec r= hat i+3 hat j+2 hat k+lambda( hat i-5 hat j+3 hat k) c. vec r= hat i+3 hat j+2 hat k+lambda( hat i+5 hat j+3 hat k) d. vec r= hat i+3 hat j+2 hat k+lambda(- hat i-5 hat j-3 hat k)

MODERN PUBLICATION-VECTOR ALGEBRA -Frequently Asked Questions (Example)
  1. If vec(a) and vec(b) are perpendicular vectors such that |vec(a)+vec(b...

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  2. Find the projection of the vector hat i+3 hat j+7 hat k on the vector...

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  3. Find lambda, when the projection of vec a=lambda hat i+ hat j+4 hat k...

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  4. If vec a and vec b are two unit vectors such that vec a+ vec b is a...

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  5. Find | vec x| , if for a unit vector vec a ,\ ( vec x-\ vec a)dot( v...

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  6. If ā,b,c are three vectors such that |veca |= 5, |vecb| = 12 and | ...

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  7. If vec(a) , vec(b) and vec(c ) be three vectors such that vec(a) + vec...

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

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

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

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

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

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

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

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

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

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

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

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

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

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