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Let vec a=5 hat i- hat j+7 hat k and v...

Let ` vec a=5 hat i- hat j+7 hat k` and ` vec b= hat i- hat j+lambda hat k` . Find `lambda` such that ` vec a+ vec b` is orthogonal to ` vec a- vec bdot`

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RD SHARMA ENGLISH-SCALAR OR DOT PRODUCT-All Questions
  1. For any two vectors vec a and vec b , show that : ( vec a+ vec b)dot...

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

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  3. Let vec a=5 hat i- hat j+7 hat k and vec b= hat i- hat j+lambda hat ...

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  4. If vec a and vec b are two vectors of the same magnitude inclined ...

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  5. Decompose the vector 6 hat i-3 hat j-6 hat k into vectors which are pa...

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  6. Express 2 hat i- hat j+3 hat k as the sum of vector parallel and a vec...

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  7. Show that the vectors vec a=3 hat i-2 hat j+ hat k , vec b= hat i+3 h...

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  8. (Projection Formulae) if a ,b ,c are the lengths of the sides opposite...

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  9. Prove using vectors: If two medians of a triangle are equal, then it i...

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  10. Find the angle between two vectors vec aa n d vec b with magnitudes s...

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  11. Find the angle between the vectors 5hat i+3 hat j+4 hat k and 6 hat i...

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  12. Find the projection of the vector 7 hat i+ hat j-4 hat kin vec a=2 hat...

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  13. For any vector vec r , prove that vec r=( vec r . hat i) hat i+( vec...

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  14. Find veca * vec b when vec a=2 hat i+2 hat j- hat ka n d vec b=6...

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  15. Find the value of lambda so that the vectors vec a=2 hat i+lambda hat...

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  16. Find the value of p for which the vectors vec a=3 hat i+2 hat j+9 ha...

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  17. Find the values of ' a ' which the vector vec r=(a^2-4) hat i+2 hat j...

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  18. If vec a , vec b , vec c are unit vector, prove that | vec a- vec b|...

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  19. If vec a , vec b , vec c are mutually perpendicular unit vectors, fin...

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  20. Find the value of c for which the vectors vec a=(clog2x) hat i-6 hat...

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