If the vectors a + b +3 c ,-2 a +3 b -4 c and a -3 b +5 c are coplanar, then the value of is

Step-by-step solution

Since, the given three vectors are coplanar, therefore one of them should be expressible as a linear combination of the remaining two ie, there exist two scalars x and y such that aligned a + b +3 c =x(-2 a +3& b -4 c ) +& y( a -3 b +5 c ) aligned On comparing the coefficient of a , b and c on both sides, we get -2 x+y=1 ; 3 x-3 y= and -4 x+5 y=3 On solving first and third equations, we get x=- 1 3 , y= 1 3 Since, the vectors are coplanar, therefore these values of x and y , also satisfy the second equation ie, -1-