1.

Find the position vector of a point R which divides the line joining the point `P(hati + 2hatj - hatk)` and `Q(-hati + hatj + hatk)` in the ratio `2 : 1`, (i) internally and (ii) externally.

Answer» Here`veca = (hati + 2hatj - hatk)` and `vecb= (-hati + hatj + hatk)`. Also `m = 2, n = 1`.
(i) When R divides PQ internally in the ratio `2 : 1`, then
position vector of `R = ((m vecb + n veca))/((m+n))`
`= (2(-hati + hatj + hatk) + 1.(hati + 2hatj - hatk))/((2+1))`
(ii) When R divides PQ externally in the ratio`2 : 1`, then
position vector of `R = ((mvecb - nveca))/((m-n))`
`= (2(-hati + hatj + hatk) + 1.(hati + 2hatj - hatk))/((2-1))`
`= (-3hati + 3hatk)`.


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