Let a =3 i + j -2 k , b =-5 i +7 j and c =3 i +y j be three vectors such that | a - b + c |= 141 . If y₁ and y₂ are the values of y satisfying the given condition, then | y ₁- y ₂ |=

Step-by-step solution

a =3 i + j -2 k , b =-5 i +7 j , c =3 i +y j aligned & a - b + c =(3 i + j -2 k )-(-5 i +7 j )+(3 i +y j ) & a - b + c =11 i +(y-6) j -2 k & | a - b + c |= 121+(y-6)^2+4 & 141 = 121+(y-6)^2+4 & 16=(y-6)^2 & y-6= 4 aligned Taking positive sign y₁-6=4 y₁=10 Taking negative sign y₂-6=-4 y₂=2 Now |y₂-y₁ |=|2-10|=8