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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. |
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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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