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Does |quad vec a|= |quad vec b| imply ve...

Does `|quad vec a|= |quad vec b|` imply `vec a= vec b`?

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Given |quad vec a|=10 , |quad vec b|=2 and vec a *vec b=12 , find | vec a cross vec b| .

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If vec a , vec b and vec c are three vectors such that vec a+vec b+vec c=vec 0 , |quad vec a|=1 , |quad vec b|=4 and |quad vec c|=2 , then find the value of vec a.vec b+vec b.vec c+vec c.vec a .

If vec a, vec b, vec c are three vectors such that |quad vec a|=5,| , quad vec b|=12 and |quad vec c|=13 and if vec a+ vec b+ vec c= 0 , find the value of vec a* vec b + vec b* vec c + vec c* vec a .

If |quad vec a+ vec b|=|quad vec a- vec b| , prove that vec a and vec b are perpendicular.

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If |quad vec a|=1 , |quad vec b|=1 and |quad vec a+ vec b|=1 , prove that | vec a- vec b|= sqrt 3 .

If vec a and vec b are two vectors such that |quad vec a + vec b|= |quad vec a| , then prove that 2 vec a+ vec b is perpendicular to the vector vec b .

If vec a , vec b and vec c are three proper vectors such that vec a * vec b=vec c , vec b*vec c=vec a . Prove that vec a , vec b , vec c are mutually at right angles and |quad vec b|=1 ,|quad vec c|=|quad vec a|.

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Is it possible that |quad vec a+ vec b|= |quad vec a|+ |quad vec b|? I...

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  2. If vec a = vec b, is it true that |quad vec a|=|quad vec b| ?

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  3. Does |quad vec a|= |quad vec b| imply vec a= vec b?

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  4. If A,B,C,D are the points with position vectors vec a,vec b, 3 vec a+ ...

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  5. If vec c= 3 vec a + 4 vec b and 2 vec c = vec a- 3 vec b, show that ve...

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  6. If the position vector of a point A is vec a + 2 vec b and vec a divi...

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  7. If ABC is triangle and D is the mid-point of [BC], prove that vec AB +...

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  8. If vec a = hat i + hat j+ 2hat k and vec b =2 hat i+ hat j - 2 hat k, ...

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  9. If vec a = 5hat i - hat j- 2hat k and vec b =5 hat i+ hat j - 2 hat k,...

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  10. If ABCD is a parallelogram and vec AB = vec a, vec BC= vec b then show...

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  11. If ABCD is a parallelogram and vec AB = vec a, vec BC= vec b then give...

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  12. ABC is any triangle and D,E,F are the mid-points of sides vec(BC),vec(...

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  13. ABCD is a parallelogram and [AC], [BD]are its diagonals. Express vec A...

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  14. ABCD is a parallelogram and [AC], [BD]are its diagonals. Express vec A...

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  15. Evaluate int dx/(x^2+10x+34)

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  16. ABCD is a parallelogram and AC, BD are its diagonals. Show that : vec(...

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  17. Apply vectors to prove that if a pair of opposite sides of quadrilater...

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  18. P is a point on the side BC of DeltaABC and Q is a point such that PQ ...

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  19. Evaluate int dx/(x^2+8x+25)

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  20. If vec a is a vectors of magnitude 3 pointing eastwards and vec b is v...

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