MHT CET20249 May 2024Evening ShiftMathematicsVector AlgebraActual
A unit vector coplanar with i + j + k and 2 i + j + k and perpendicular to i + j - k is
Options
- A+ 1 2 (- j - k )
- B( j - k ) 2
- C- j +2 k 5
- D+ 1 26 ( j +5 k )
Correct answer
A. + 1 2 (- j - k )
Step-by-step solution
Let a = i + j - k , b = i + j + k , c =2 i + j + k . Then, required unit vectors are given by = a ( b c ) | a ( b c )| Now, a ( b c )=( a c ) b -( a b ) c array ll & =2( i + j + k )-1(2 i + j + k )= j + k & | a ( b c )|= 1+1 = 2 array Hence, required unit vectors are = j + k 2