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Find the position vector of the point R...

Find the position vector of the point R which divides the line (segment) joining the two points P and Q with position vectors `vec(OP) = 2 vec a+ vec b` and `vec (OQ) = vec a-2 vec b` respectively, in the ratio 1: 2. (i) internally (ii) externally. ‘

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the angle between the vectors 2 hat i -hat j+ hat k and 3 hat i +...

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  2. Find a vector of magnitude 11 in the direction opposite to that of vec...

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  3. Find the position vector of the point R which divides the line (segme...

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  4. if vec a = 2 hat i - hat j+ hat k, vec b =hat i+ hat j - 2 hat k and ...

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  5. Find the magnitude of a vector, whose components are 3, 4 and -12

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  6. Consider the points P (- 1, 0 2) and Q (3, -2 1), Write down vector v...

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  7. If vec a = 2hat i - hat j+ 3hat k and vec b =4 hat i+ hat j - 3 hat k,...

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  8. For any two vectors vec a and vec b, prove that (vec a* vec b)^ 2 le |...

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  9. If for a vector vec a, vec a*hat i = vec a*hat j= vec a*hat k=0, then ...

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  10. If |vec a|=10, and |vec b|=2 and vec a* vec b =12, find angle between ...

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  11. What is the area of a triangle, two of whose sides are along the vecto...

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  12. If vec a and vec b are the position vectors of A and B respectively, f...

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  13. Evaluate int sin2x dx/(1-sinx)

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  14. Find the sine of the angle between the vectors vec a =3 hat i+hat j+2 ...

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  15. Find a vector of magnitude 6 units which is at right angles to both th...

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  16. A vector vec(r ) is inclined at equal angles to the three axes. If the...

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  17. If vec a = 6hat i - hat j+ 2hat k and vec b =hat i- 3hat j - 2 hat k, ...

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  18. What is the value of [vec a vec b vec c] if vec a, vec b, vec c are no...

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  19. If a and b are two unit vectors such that a+2b and 5a−4b are perpendic...

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  20. If vec a = 7 hat i +hat j - 4 hat kand vec b=2 hat i+6 hat j +3 hat k,...

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