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If vec c= 3 vec a + 4 vec b and 2 vec c ...

If `vec c= 3 vec a + 4 vec b` and `2 vec c = vec a- 3 vec b`, show that `vec c` and `vec b` have opposite directions and `|quad vec c|> 2|quad vec b|`.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Does |quad vec a|= |quad vec b| imply vec a= vec b?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Evaluate int dx/(x^2+12x+37)

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  20. integrate the following int dx/(x^2+10x+16)

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