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

Let ` vec a=x^2 hat i+2 hat j-2 hat k ,\ vec b= hat i- hat j+ hat k\ a n d\ vec c=x^2 hat i+5 hat j-4 hat k` be three vecrors find the values of `x` for which the angle between ` vec a\ a n d\ vec b` acute and the angle between ` vec b\ a n d\ vec c` is obtuse.

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Let vec a=x^2 hat i+2 hat j-2 hat k , vec b= hat i- hat j+ hat k and vec c=x^2 hat i+5 hat j-4 hat k be three vectors. Find the values of x for which the angle between vec a and vec b is acute and the angle between vec b and vec c is obtuse.

Find the sum of vectors vec a= hat i-2 hat j+ hat k ,\ vec b=-2 hat i+4 hat j+5 hat k\ a n d\ vec c= hat i-6 hat j-7 hat kdot

Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 hat i+4 hat j-2 hat k\ a n d\ vec c=4 hat i-2 hat j-2 hat k are coplanar.

If vec a=x hat i+y hat j+z hat k , vec b=y hat i+z hat j+x hat k and vec c=z hat i+x hat j+y hat k , then vec axx( vec bxx vec c) is

Find vec adot vec b when: vec a= hat i-2 hat j+ hat k\ a n d\ vec b=4 hat i-4 hat j+7 hat k

Find vec adot vec b when: vec a= hat j- hat k\ a n d\ vec b=2 hat i+3 hat j-2 hat k

If vec a= hat i+ hat j- hat k ,\ vec b=- hat i+2 hat j+2 hat k\ a n d\ vec c=- hat i+2 hat j- hat k , then a unit vector normal to the vectors a+b\ a n d\ b-c is

If vec a=3 hat i- hat j-4 hat k , vec b=2 hat i+4 hat j-3 hat k and vec c= hat i+2 hat j- hat k , find |3 vec a-2 hat b+4 hat c|dot

If vec a= hat i+ hat j+ hat k ,\ vec b=2 hat i- hat j+3 hat k\ a n d\ vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec c

Find | vec a xx vec b|, if vec a=2 hat i+ hat j+3 hat k and vec b=3 hat i+5 hat j-2 hat k .

RD SHARMA ENGLISH-SCALAR OR DOT PRODUCT-All Questions
  1. If vec a+ vec b+ vec c= vec0, show that the angle theta between the v...

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

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  3. 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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  4. 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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  5. If vec a\ a n d\ vec b are two non collinear unit vectors such that ...

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

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

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

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

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

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

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  13. (Pythagoras’s Theorem) Prove by vector method that in a right angle...

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  14. Prove by vector method that the sum of the square of the diagonals ...

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  15. prove using vectors: The quadrilateral obtained by joining mid-poin...

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  16. Using analytical geometry, prove that the diagonals of a rhombus are ...

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  17. Prove that the diagonals of a rectangle are perpendicular if and on...

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  18. In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C...

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  19. If the median to the base of a triangle is perpendicular to the bas...

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  20. In a quadrilateral A B C D , prove that A B^2+B C^2+C D^2+D A^2=A C^2+...

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