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Let vec a=5 hat i- hat j+7 hat k\ a n d...

Let ` vec a=5 hat i- hat j+7 hat k\ a n d\ vec b= hat i- hat j+lambda hat kdot` Find `lambda` such that ` vec a+ vec b` is orthogonal to ` vec a- vec bdot`

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

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

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

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  4. If vec adot vec a=0\ a n d\ vec adot vec b=0\ what can you conclud...

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  5. If vec c is perpendicular to both vec a\ a n d\ vec b , then prove ...

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  6. If | vec a|= a\ a n d\ | vec b|=b, prove that ( vec a/(a^2)- vec b/(b^...

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  7. If vec a ,\ vec b ,\ vec c are three non coplanar vectors such that...

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  8. If a vector vec a is perpendicular to two non collinear vectors vec ...

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  9. If vec a+ vec b+ vec c= vec0, show that the angle theta between the v...

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  10. Let vec u ,\ vec v\ a n d\ vec w be vector such vec u+ vec v+ vec ...

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

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  12. Find the value of x\ a n d\ y if the vectors vec a=3 hat i+x hat j- h...

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  13. If vec a\ a n d\ vec b are two non collinear unit vectors such that ...

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  14. If vec a ,\ vec b are two vectors such that | vec a+ vec b|\ =| vec ...

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  15. Prove using vectors: The median to the base of an isosceles triangl...

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  16. Show that the diagonals of a rhombus bisect each other at right ang...

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  17. Using vector method, prove that the angel in a semi circle is a rig...

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  18. Prove that the cosine formula for triangles is equivalent to the de...

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  19. In a triangle O A B ,\ /A O B=90^0dot If P\ a n d\ Q are points of tri...

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  20. Prove that; If the diagonals of a quadrilateral bisect each other a...

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