34 Consider the vectors u = < -10, 9, - 7>,? v =1119w = <88submit your answer as a fraction, if necessary. (The use of a computer algebra system may be used to reduceany matrices involved.)k ="Question Help: VideoSubmit Question< − 9, − 1, −9>, and-k > . What value of k will cause the set {ū, v, w} to be linearly dependent? You may2makes the set linearly dependent.

three vectors u→,v→,w→ will be linearly dependent when for some non zero constant a,b,c au→+bv→+cw→=0 Which is possible only when u→,v→,w→ are co planer three vectors will be coplanar only when their scalar triple product is zero ' u→,v→,w→ will be co planer when u→. v→×w→=0 So finally we can conclude three vectors u→,v→,w→ will be linearly dependent when u→. v→×w→=0 ...... (1)Here given vectors are u→=-10 , 9 , -7v→= -9 , -1 , -9 w→=118,-198,k scaler triple product u→. v→×w→=-109-7-9-1-9118-198k = -10 -1×k--9×-198-9-9×k--9×118-7 -9×-198--1×118 = -10 -k-1718-9-9k+998-7 1718+118 = 10k+17108+81k-8918-12748 = 91k-4558For linear dependence u→. v→×w→ =0 91k-4558=091k =4558k =4558×91=455728 So value of k for which given vectors are linearly dependent k=455728