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Let a, b and c be three non-zero vectors which are pairwise non-collinear. If a+3b is collinear with c and b+2c is collinear with a then a+3b+6cis |
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Answer» `a+c` `rArr a + 3B= LAMBDA c "….."(i)` Also, `b + 3c`is collinearwith a. `rArr b + 2C = MUA "…"(ii)` From Eq. (i) we get `a + 3b + 6C= (lambda + 6) c "….."(ii)` From Eq. (ii), we get `a+ 3b +6 c= (1+3 mu) a"....."(iv)` On solvingEqs. (iii) and (iv) , we get `(lambda + 6) c = (1+3 mu) a` Since, a is not collinear with c. `rArr lambda + 6= 1 + 3 mu = 0` From Eq. (v), we get `a+ 3b + 6 c = 0` |
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