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                                    Let a, b and c be three non-zero vectors such that no two of these are collinear. If the vector a+2b is collinear with c and b+3c is collinear with a (lambda being some non-zero scalar), then a+2b+6c equals to | 
                            
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Answer»  `lambdaa` `a + 2b = tc "…"(i)` Also, `b+3c` is collinearwith a, then `b + 3c = lambda` `RARR b= lambda a - 3c "…."(iii)` From Eqs. (i) and (ii), we get `a+ 2(lambdaa- 3c) = t c` `rArr (a-6c) = t c - 2lambda a` On comparingthe COEFFICIENTS of a and b,we get `1= -2lambda` `rArr lambda = - 1/2 ` and `- 6 = t` `rArr t = - 6` `rArrt = - 6` From Eq. (i) we get `a + 2b = -6c` `rArr a + 2b+6c = 0`  | 
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