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12). Show that the vector hat i+ hat j...

12). Show that the vector ` hat i+ hat j+ hat k` is equally inclined with the coordinate axes. (13)show that the vectors `veca=1/7(2hati+3hatj+6hatk),vecb=1/7(3hati-6hatj+2hatk),vecc=1/7(6hati+2hatj-3hatk)` are mutually perpendicular unit vectors.

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Find the sum of the vectors vec=hati-2hatj+hatk, vecb=-2hati+4 hatj+5hatk and vecc=hati-6hatj-7hatk

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Find the unit vector in the direction of the sum of the vectors veca=2hati+2hatj-5hatk and vecb=2hati+hatj+3hatk .

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RD SHARMA ENGLISH-SCALAR OR DOT PRODUCT-All Questions
  1. Let vec u , vec v and vec w be vector such vec u+ vec v+ vec w...

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  2. Let vec a=x^2 hat i+2 hat j-2 hat k , vec b= hat i- hat j+ hat k and ...

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  3. 12). Show that the vector hat i+ hat j+ hat k is equally inclined w...

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  4. If vecalpha=3 hat i+4 hat j+5 hat k and vecbeta=2 hat i+ hat j-4 ha...

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

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  6. For any two vectors vec a and vec b , show that : ( vec a+ vec b)dot...

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

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

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

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

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

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

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

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

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

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

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

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

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

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