COMEDK2023MathematicsVector Algebra
a =2 i + j - k , b = i - j and c =5 i - j + k , then unit vector parallel to a + b - c but in opposite direction is
Options
- A1 3 (2 i - j +2 k )
- B1 2 (2 i - j +2 k )
- C1 3 (2 i - j -2 k )
- DNone of these
Correct answer
A. 1 3 (2 i - j +2 k )
Step-by-step solution
Given, a =2 i + j - k , b = i - j and c =5 i - j + k aligned : a + b - c & =(2+1-5) i +(1-1+1) j +(-1+0-1) k & =-2 i + j -2 k =-(2 i - j +2 k ) aligned Now, the unit vector in the direction of a + b - c be -(2 i - j +2 k ) 2^2+(-1)^2+2^2 =- 1 3 (2 i - j +2 k ) The required unit vector be 1 3 (2 i - j +2 k ) .