If the vectors a =2 i -3 j +4 k , b = i +2 j - k and c =m i - j +2 k are coplanar, then the value of m is

Step-by-step solution

Since, vectors a, b and c are coplanar [ a b c ]=0 a ( b c )=0 Now, aligned b c & = | array ccc i & j & k 1 & 2 & -1 m & -1 & 2 array | & = i (4-1)- j (2+m)+ k (-1-2 m) & =3 i -(2+m) j -(1+2 m) k aligned aligned a ( b c ) & =(2 i -3 j +4 k ) (3 i -(2+m) j -(1+2 m) k ) & =2(3)+3(2+m)-4(1+2 m) & =6+6+3 m-4-8 m=8-5 m & a ( b c )=0 & 8-5 m=0 m= 8 5 aligned and aligned a ( b c ) & =(2 i -3 j +4 k ) (3 i -(2+m) j -(1+2 m) k ) & =2(3)+3(2+m)-4(1+2 m) & =6+6+3 m-4-8 m=8-5 m & a ( b c )=0 & 8-5 m=0 m= 8 5 aligned