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If vec p=5 hat i+lambda hat j-3 hat k\ ...

If ` vec p=5 hat i+lambda hat j-3 hat k\ a n d\ vec q= hat i+3 hat j-5 hat k ,` then find the value of `lambda` such that ` vec p+ vec q` and ` vec p- vec q` are perpendicular vectors.

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The correct Answer is:
`pm 1`
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MODERN PUBLICATION-VECTOR ALGEBRA -EXERCISE 10 (e ) Long Answer Type Questions (I)
  1. If vectors vec a=2 hat i+2 hat j+3 hat k ,\ vec b=- hat i+2 hat j+ h...

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  2. If vec a= hat a= hat i-\ hat j+7 hat k and vec b=5 hat j-\ hat j+l...

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  3. If vec p=5 hat i+lambda hat j-3 hat k\ a n d\ vec q= hat i+3 hat j-5...

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  4. If vec(a)=5hat(i)-hat(j)+7hat(k) and vec(b)=hat(i)-hat(j)-lambda ha...

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  5. If vec(a)=3hat(i)+hat(j)+9hat(k) and vec(b)=hat(i)+lambda hat(j)+3ha...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. 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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