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If vec r1, vec r2, vec r3 are the posit...

If ` vec r_1, vec r_2, vec r_3` are the position vectors off thee collinear points and scalar `pa n dq` exist such that ` vec r_3=p vec r_1+q vec r_2,` then show that `p+q=1.`

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`vec(r_3)= p vec(r_1)+q (r_2)`
`" "=(pvec(r_1)+ (1-p)vec(r_2))/(p+ (1+p))`
`vec(r_3)` divides `vec(r_1)` in the ratios `(1-p): p`
Hence, `vec(r_1), vec(r_2) and vec(r_3)` are collinear.
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CENGAGE-INTRODUCTION TO VECTORS -Exercise 1.1
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  3. Find the direction cosines of the vector joining the points A(1, 2,3) ...

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  4. The position vectors of Pa n dQ are 5 hat i+4 hat j+a hat k and - hat ...

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  6. Find a vector of magnitude 5 units and parallel to the resultant of th...

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  7. Show that the points A(1, -2, -8) B (5, 0, -2) and C(11, 3, 7) are col...

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  8. If A B C D is a rhombus whose diagonals cut at the origin O , then ...

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  9. Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , re...

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  10. Let A B C D be a p[arallelogram whose diagonals intersect at P and ...

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  11. If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n d...

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  12. If vec A O+ vec O B= vec B O+ vec O C , then A ,Bn a dC are (where O ...

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  13. If the sides of an angle are given by vectors veca=hati-2hatj+2hatk an...

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  14. A B C D is a parallelogram. If La n dM are the mid-points of B Ca n dD...

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  15. A B C D is a quadrilateral. E is the point of intersection of th...

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  16. What is the unit vector parallel to vec a=3 hat i+4 hat j-2 hat k ...

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  17. The position vectors of points Aa n dB w.r.t. the origin are vec a...

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  18. If vec r1, vec r2, vec r3 are the position vectors off thee collinear...

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  19. If veca and vecb are two vectors of magnitude 1 inclined at 120^(@), t...

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