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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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The correct Answer is:
`lambda =5`
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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 -EXERCISE 10 (e ) Short Answer Type Questions
  1. If either vector -> a= ->0 or -> b= ->0 , then -> adot -> b=0...

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  2. Find the scalar projection of : vec(a)=7hat(i)+hat(j)-4hat(k) on v...

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  3. Find the scalar projection of : vec(a)=3hat(i)-2hat(j)+hat(k) on ...

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  4. Find the scalar projection of : vec(a)=2hat(i)+3hat(j)+2hat(k) on ...

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  5. Find the scalar projection of : vec(a)=hat(i)-hat(j) on vec(b)=hat...

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  6. Find the scalar projection of : vec(a)=hat(i)+3hat(j)+7hat(k) on ...

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  7. Find the scalar projection of vec(b) on vec(a), when : vec(a)=2hat(...

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  8. Find the scalar projection of vec(b) on vec(a), when : vec(a)=2hat(...

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  9. Find the vector projection of the vector : 7hat(i)+hat(j)-hat(k) ...

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  10. Find the vector projection of the vector : 2hat(i)-hat(j)+hat(k) ...

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

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  12. Show that the vector vec a=1/7(2 hat i+3 hat j+6 hat k),\ vec b=1/7(...

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  13. If vec(a)=5hat(i)-hat(j)-3hat(k) and vec(b)=hat(i)+3hat(j)-5hat(k), t...

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  14. If vec(a)=hat(i)+2hat(j)-3hat(k) and vec(b)=3hat(i)-hat(j)+2hat(k), t...

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  15. Write the value of 'p' for which : vec(a)=3hat(i)+2hat(j)+9hat(k) and...

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  16. Find the value of 'lambda' such that the vectors vec(a) and vec(b) a...

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  17. Find the value of 'lambda' such that the vectors vec(a) and vec(b) a...

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  18. If 2hat(i)+hat(j)-3hat(k) and m hat(i)+3hat(j)-hat(k) are perpendicu...

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  19. Show that the projection of vec(b) on vec(a) ne vec(0) is : ((vec(...

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  20. Show that |vec(a)|vec(b)-|vec(b)|vec(a), for any two non - zero vector...

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